ANALYTICAL CHEMISTRY Analytical Chemistry This text is disseminated via the Open Education Resource (OER) LibreTexts Project (https://LibreTexts.org) and like the hundreds of other texts available within this powerful platform, it is freely available for reading, printing and "consuming." Most, but not all, pages in the library have licenses that may allow individuals to make changes, save, and print this book. Carefully consult the applicable license(s) before pursuing such effects. Instructors can adopt existing LibreTexts texts or Remix them to quickly build course-specific resources to meet the needs of their students. Unlike traditional textbooks, LibreTexts’ web based origins allow powerful integration of advanced features and new technologies to support learning. 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This text was compiled on 01/12/2024 TABLE OF CONTENTS Licensing 2: Analytical Chemistry 2.0 (Harvey) 00: Front Matter Table of Contents 1: Front Matter 1.1: TitlePage 1.2: InfoPage 1.3: Table of Contents 2: Introduction to Analytical Chemistry 2.2: The Analytical Perspective 2.3: Common Analytical Problems 2.4: Introduction to Analytical Chemistry (Exercises) 2.5: Introduction to Analytical Chemistry (Summary) 3: Basic Tools of Analytical Chemistry 3.1: Measurements in Analytical Chemistry 3.2: Concentration 3.3: Stoichiometric Calculations 3.4: Basic Equipment 3.5: Preparing Solutions 3.6: Spreadsheets and Computational Software 3.7: The Laboratory Notebook 3.8: Basic Tools of Analytical Chemistry (Exercises) 3.9: Basic Tools of Analytical Chemistry (Summary) 4: The Vocabulary of Analytical Chemistry 4.1: Analysis, Determination, and Measurement 4.2: Techniques, Methods, Procedures, and Protocols 4.3: Classifying Analytical Techniques 4.4: Selecting an Analytical Method 4.5: Developing the Procedure 4.6: Protocols 4.7: The Importance of Analytical Methodology 4.8: The Vocabulary of Analytical Chemistry (Exercises) 4.9: The Vocabulary of Analytical Chemistry (Summary) 5: Evaluating Analytical Data 5.1: Characterizing Measurements and Results 5.2: Characterizing Experimental Errors 5.3: Propagation of Uncertainty 5.4: The Distribution of Measurements and Results 5.5: Statistical Analysis of Data 5.6: Statistical Methods for Normal Distributions 5.7: Detection Limits 5.8: Using Excel and R to Analyze Data 5.9: Evaluating Analytical Data (Exercises) 5.10: Evaluating Analytical Data (Summary) 1 https://chem.libretexts.org/@go/page/191313 6: Standardizing Analytical Methods 6.1: Analytical Standards 6.2: Calibrating the Signal 6.3: Determining the Sensitivity 6.4: Linear Regression and Calibration Curves 6.5: Blank Corrections 6.6: Using Excel and R for a Regression Analysis 6.7: Standardizing Analytical Methods (Exercises) 6.8: Standardizing Analytical Methods (Summary) 7: Equilibrium Chemistry 7.1: Reversible Reactions and Chemical Equilibria 7.2: Thermodynamics and Equilibrium Chemistry 7.3: Manipulating Equilibrium Constants 7.4: Equilibrium Constants for Chemical Reactions 7.5: Le Châtelier’s Principle 7.6: Ladder Diagrams 7.7: Solving Equilibrium Problems 7.8: Buffer Solutions 7.9: Activity Effects 7.10: Using Excel and R to Solve Equilibrium Problems 7.11: Some Final Thoughts on Equilibrium Calculations 7.12: Equilibrium Chemistry (Exercises) 7.13: Equilibrium Chemistry (Summary) 8: Collecting and Preparing Samples 8.1: The Importance of Sampling 8.2: Designing a Sampling Plan 8.3: Implementing the Sampling Plan 8.4: Separating the Analyte from Interferents 8.5: General Theory of Separation Efficiency 8.6: Classifying Separation Techniques 8.7: Liquid–Liquid Extractions 8.8: Separation Versus Preconcentration 8.9: Collecting and Preparing Samples (Exercises) 8.10: Collecting and Preparing Samples (Summary) 9: Gravimetric Methods 9.1: Overview of Gravimetric Methods 9.2: Precipitation Gravimetry 9.3: Volatilization Gravimetry 9.4: Particulate Gravimetry 9.5: Gravimetric Methods (Exercises) 9.6: Gravimetric Methods (Summary) 10: Titrimetric Methods 10.1: Overview of Titrimetry 10.2: Acid–Base Titrations 10.3: Complexation Titrations 10.4: Redox Titrations 10.5: Precipitation Titrations 10.6: Titrimetric Methods (Exercises) 10.7: Titrimetric Methods (Summary) 11: Spectroscopic Methods 2 https://chem.libretexts.org/@go/page/191313 11.1: Overview of Spectroscopy 11.2: Spectroscopy Based on Absorption 11.03: UV 11.3: UV/Vis and IR Spectroscopy 11.4: Atomic Absorption Spectroscopy 11.5: Emission Spectroscopy 11.6: Photoluminescence Spectroscopy 11.7: Atomic Emission Spectroscopy 11.8: Spectroscopy Based on Scattering 11.9: Spectroscopic Methods (Exercises) 11.10: Spectroscopic Methods (Summary) 12: Electrochemical Methods 12.1: Overview of Electrochemistry 12.2: Potentiometric Methods 12.3: Coulometric Methods 12.4: Voltammetric Methods 12.5: Electrochemical Methods (Exercises) 12.6: Electrochemical Methods (Summary) 13: Chromatographic 13.1: Overview of Analytical Separations 13.2: General Theory of Column Chromatography 13.3: Optimizing Chromatographic Separations 13.4: Gas Chromatography 13.5: High-Performance Liquid Chromatography 13.6: Other Forms of Liquid Chromatography 13.7: Electrophoresis 13.8: Chromatographic and Electrophoretic Methods (Exercises) 13.9: Chromatographic and Electrophoretic Methods (Summary) 14: Kinetic Methods 14.1: Kinetic Methods Versus Equilibrium Methods 14.2: Chemical Kinetics 14.3: Radiochemistry 14.4: Flow Injection Analysis 14.5: Kinetic Methods (Exercises) 14.6: Kinetic Methods (Summary) 15: Developing a Standard Method 15.1: Optimizing the Experimental Procedure 15.2: Verifying the Method 15.3: Validating the Method as a Standard Method 15.4: Using Excel and R for an Analysis of Variance 15.5: Developing a Standard Method (Exercises) 15.6: Developing a Standard Method (Summary) 16: Quality Assurance 16.1: The Analytical Perspective—Revisited 16.2: Quality Control 16.3: Quality Assessment 16.4: Evaluating Quality Assurance Data 16.5: Quality Assurance (Exercises) 17: Additional Resources 18: Back Matter 3 https://chem.libretexts.org/@go/page/191313 Index Glossary Detailed Licensing 4 https://chem.libretexts.org/@go/page/191313 Licensing A detailed breakdown of this resource's licensing can be found in Back Matter/Detailed Licensing. 1 https://chem.libretexts.org/@go/page/417429 00: Front Matter This page was auto-generated because a user created a sub-page to this page. 00.1 https://chem.libretexts.org/@go/page/200590 TABLE OF CONTENTS 00: Front Matter Table of Contents 1: Front Matter 1.1: TitlePage 1.2: InfoPage 1.3: Table of Contents 2: Introduction to Analytical Chemistry 2.2: The Analytical Perspective 2.3: Common Analytical Problems 2.4: Introduction to Analytical Chemistry (Exercises) 2.5: Introduction to Analytical Chemistry (Summary) 3: Basic Tools of Analytical Chemistry 3.1: Measurements in Analytical Chemistry 3.2: Concentration 3.3: Stoichiometric Calculations 3.4: Basic Equipment 3.5: Preparing Solutions 3.6: Spreadsheets and Computational Software 3.7: The Laboratory Notebook 3.8: Basic Tools of Analytical Chemistry (Exercises) 3.9: Basic Tools of Analytical Chemistry (Summary) 4: The Vocabulary of Analytical Chemistry 4.1: Analysis, Determination, and Measurement 4.2: Techniques, Methods, Procedures, and Protocols 4.3: Classifying Analytical Techniques 4.4: Selecting an Analytical Method 4.5: Developing the Procedure 4.6: Protocols 4.7: The Importance of Analytical Methodology 4.8: The Vocabulary of Analytical Chemistry (Exercises) 4.9: The Vocabulary of Analytical Chemistry (Summary) 5: Evaluating Analytical Data 5.1: Characterizing Measurements and Results 5.2: Characterizing Experimental Errors 5.3: Propagation of Uncertainty 5.4: The Distribution of Measurements and Results 5.5: Statistical Analysis of Data 5.6: Statistical Methods for Normal Distributions 5.7: Detection Limits 5.8: Using Excel and R to Analyze Data 1 https://chem.libretexts.org/@go/page/200591 5.9: Evaluating Analytical Data (Exercises) 5.10: Evaluating Analytical Data (Summary) 6: Standardizing Analytical Methods 6.1: Analytical Standards 6.2: Calibrating the Signal 6.3: Determining the Sensitivity 6.4: Linear Regression and Calibration Curves 6.5: Blank Corrections 6.6: Using Excel and R for a Regression Analysis 6.7: Standardizing Analytical Methods (Exercises) 6.8: Standardizing Analytical Methods (Summary) 7: Equilibrium Chemistry 7.1: Reversible Reactions and Chemical Equilibria 7.2: Thermodynamics and Equilibrium Chemistry 7.3: Manipulating Equilibrium Constants 7.4: Equilibrium Constants for Chemical Reactions 7.5: Le Châtelier’s Principle 7.6: Ladder Diagrams 7.7: Solving Equilibrium Problems 7.8: Buffer Solutions 7.9: Activity Effects 7.10: Using Excel and R to Solve Equilibrium Problems 7.11: Some Final Thoughts on Equilibrium Calculations 7.12: Equilibrium Chemistry (Exercises) 7.13: Equilibrium Chemistry (Summary) 8: Collecting and Preparing Samples 8.1: The Importance of Sampling 8.2: Designing a Sampling Plan 8.3: Implementing the Sampling Plan 8.4: Separating the Analyte from Interferents 8.5: General Theory of Separation Efficiency 8.6: Classifying Separation Techniques 8.7: Liquid–Liquid Extractions 8.8: Separation Versus Preconcentration 8.9: Collecting and Preparing Samples (Exercises) 8.10: Collecting and Preparing Samples (Summary) 9: Gravimetric Methods 9.1: Overview of Gravimetric Methods 9.2: Precipitation Gravimetry 9.3: Volatilization Gravimetry 9.4: Particulate Gravimetry 9.5: Gravimetric Methods (Exercises) 9.6: Gravimetric Methods (Summary) 2 https://chem.libretexts.org/@go/page/200591 10: Titrimetric Methods 10.1: Overview of Titrimetry 10.2: Acid–Base Titrations 10.3: Complexation Titrations 10.4: Redox Titrations 10.5: Precipitation Titrations 10.6: Titrimetric Methods (Exercises) 10.7: Titrimetric Methods (Summary) 11: Spectroscopic Methods 11.1: Overview of Spectroscopy 11.2: Spectroscopy Based on Absorption 11.03: UV 11.3: UV/Vis and IR Spectroscopy 11.4: Atomic Absorption Spectroscopy 11.5: Emission Spectroscopy 11.6: Photoluminescence Spectroscopy 11.7: Atomic Emission Spectroscopy 11.8: Spectroscopy Based on Scattering 11.9: Spectroscopic Methods (Exercises) 11.10: Spectroscopic Methods (Summary) 12: Electrochemical Methods 12.1: Overview of Electrochemistry 12.2: Potentiometric Methods 12.3: Coulometric Methods 12.4: Voltammetric Methods 12.5: Electrochemical Methods (Exercises) 12.6: Electrochemical Methods (Summary) 13: Chromatographic 13.1: Overview of Analytical Separations 13.2: General Theory of Column Chromatography 13.3: Optimizing Chromatographic Separations 13.4: Gas Chromatography 13.5: High-Performance Liquid Chromatography 13.6: Other Forms of Liquid Chromatography 13.7: Electrophoresis 13.8: Chromatographic and Electrophoretic Methods (Exercises) 13.9: Chromatographic and Electrophoretic Methods (Summary) 14: Kinetic Methods 14.1: Kinetic Methods Versus Equilibrium Methods 14.2: Chemical Kinetics 14.3: Radiochemistry 14.4: Flow Injection Analysis 14.5: Kinetic Methods (Exercises) 14.6: Kinetic Methods (Summary) 3 https://chem.libretexts.org/@go/page/200591 15: Developing a Standard Method 15.1: Optimizing the Experimental Procedure 15.2: Verifying the Method 15.3: Validating the Method as a Standard Method 15.4: Using Excel and R for an Analysis of Variance 15.5: Developing a Standard Method (Exercises) 15.6: Developing a Standard Method (Summary) 16: Quality Assurance 16.1: The Analytical Perspective—Revisited 16.2: Quality Control 16.3: Quality Assessment 16.4: Evaluating Quality Assurance Data 16.5: Quality Assurance (Exercises) 17: Additional Resources 18: Back Matter 4 https://chem.libretexts.org/@go/page/200591 CHAPTER OVERVIEW 1: Front Matter 1.1: TitlePage 1.2: InfoPage 1.3: Table of Contents 1 DePauw University Analytical Chemistry 2.1 David Harvey This text is disseminated via the Open Education Resource (OER) LibreTexts Project (https://LibreTexts.org) and like the hundreds of other texts available within this powerful platform, it is freely available for reading, printing and "consuming." Most, but not all, pages in the library have licenses that may allow individuals to make changes, save, and print this book. Carefully consult the applicable license(s) before pursuing such effects. Instructors can adopt existing LibreTexts texts or Remix them to quickly build course-specific resources to meet the needs of their students. Unlike traditional textbooks, LibreTexts’ web based origins allow powerful integration of advanced features and new technologies to support learning. The LibreTexts mission is to unite students, faculty and scholars in a cooperative effort to develop an easy-to-use online platform for the construction, customization, and dissemination of OER content to reduce the burdens of unreasonable textbook costs to our students and society. The LibreTexts project is a multi-institutional collaborative venture to develop the next generation of openaccess texts to improve postsecondary education at all levels of higher learning by developing an Open Access Resource environment. The project currently consists of 14 independently operating and interconnected libraries that are constantly being optimized by students, faculty, and outside experts to supplant conventional paper-based books. These free textbook alternatives are organized within a central environment that is both vertically (from advance to basic level) and horizontally (across different fields) integrated. The LibreTexts libraries are Powered by NICE CXOne and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. This material is based upon work supported by the National Science Foundation under Grant No. 1246120, 1525057, and 1413739. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation nor the US Department of Education. Have questions or comments? For information about adoptions or adaptions contact info@LibreTexts.org. More information on our activities can be found via Facebook (https://facebook.com/Libretexts), Twitter (https://twitter.com/libretexts), or our blog (http://Blog.Libretexts.org). This text was compiled on 01/12/2024 1.3: Table of Contents Analytical chemistry spans nearly all areas of chemistry but involves the development of tools and methods to measure physical properties of substances and apply those techniques to the identification of their presence (qualitative analysis) and quantify the amount present (quantitative analysis) of species in a wide variety of settings. 1: Introduction to Analytical Chemistry 1.1: What is Analytical Chemistry? 1.2: The Analytical Perspective 1.3: Common Analytical Problems 1.E: Introduction to Analytical Chemistry (Exercises) 1.S: Introduction to Analytical Chemistry (Summary) 2: Basic Tools of Analytical Chemistry In the chapters that follow we will explore many aspects of analytical chemistry. In the process we will consider important questions such as “How do we treat experimental data?”, “How do we ensure that our results are accurate?”, “How do we obtain a representative sample?”, and “How do we select an appropriate analytical technique?” Before we look more closely at these and other questions, we will first review some basic tools of importance to analytical chemists. 2.1: Measurements in Analytical Chemistry 2.2: Concentration 2.3: Stoichiometric Calculations 2.4: Basic Equipment 2.5: Preparing Solutions 2.6: Spreadsheets and Computational Software 2.7: The Laboratory Notebook 2.E: Basic Tools of Analytical Chemistry (Exercises) 2.S: Basic Tools of Analytical Chemistry (Summary) 3: The Vocabulary of Analytical Chemistry If you leaf through an issue of the journal Analytical Chemistry, you will soon discover that the authors and readers share a common vocabulary of analytical terms. You are probably familiar with some of these terms, such as accuracy and precision, but other terms, such as analyte and matrix may be less familiar to you. In order to participate in the community of analytical chemists, you must first understand its vocabulary. 3.1: Analysis, Determination, and Measurement 3.2: Techniques, Methods, Procedures, and Protocols 3.3: Classifying Analytical Techniques 3.4: Selecting an Analytical Method 3.5: Developing the Procedure 3.6: Protocols 3.7: The Importance of Analytical Methodology 3.E: The Vocabulary of Analytical Chemistry (Exercises) 3.S: The Vocabulary of Analytical Chemistry (Summary) 4: Evaluating Analytical Data When using an analytical method we make three separate evaluations of experimental error. First, before beginning an analysis we evaluate potential sources of errors to ensure that they will not adversely effect our results. Second, during the analysis we monitor our measurements to ensure that errors remain acceptable. Finally, at the end of the analysis we evaluate the quality of the measurements and results, comparing them to our original design criteria. 4.1: Characterizing Measurements and Results 4.2: Characterizing Experimental Errors 1.3.1 https://chem.libretexts.org/@go/page/190264 4.3: Propagation of Uncertainty 4.4: The Distribution of Measurements and Results 4.5: Statistical Analysis of Data 4.6: Statistical Methods for Normal Distributions 4.7: Detection Limits 4.8: Using Excel and R to Analyze Data 4.E: Evaluating Analytical Data (Exercises) 4.S: Evaluating Analytical Data (Summary) 5: Standardizing Analytical Methods Standardization is the process of determining the relationship between the signal and the amount of analyte in a sample. Previously, we defined this relationship as Stotal=kACA+Sreag where Stotal is the signal, nA is the moles of analyte, CA is the analyte’s concentration, kA is the method’s sensitivity for the analyte, and Sreag is the contribution to Stotal from sources other than the sample. To standardize a method we must determine values for kA and Sreag, which is the subject of this chapt 5.1: Analytical Standards 5.2: Calibrating the Signal 5.3: Determining the Sensitivity 5.4: Linear Regression and Calibration Curves 5.5: Blank Corrections 5.6: Using Excel and R for a Regression Analysis 5.E: Standardizing Analytical Methods (Exercises) 5.S: Standardizing Analytical Methods (Summary) 6: Equilibrium Chemistry Regardless of the problem on which an analytical chemist is working, its solution requires a knowledge of chemistry and the ability to apply that knowledge. For example, an analytical chemist studying the effect of pollution on spruce trees needs to know the chemical differences between p‑hydroxybenzoic acid and p‑hydroxyacetophenone, two phenols found in the needles of spruce trees. Your ability to “think as a chemist” is a product of your experience in the classroom and in the laboratory. 6.1: Reversible Reactions and Chemical Equilibria 6.2: Thermodynamics and Equilibrium Chemistry 6.3: Manipulating Equilibrium Constants 6.4: Equilibrium Constants for Chemical Reactions 6.5: Le Châtelier’s Principle 6.6: Ladder Diagrams 6.7: Solving Equilibrium Problems 6.8: Buffer Solutions 6.9: Activity Effects 6.10: Using Excel and R to Solve Equilibrium Problems 6.11: Some Final Thoughts on Equilibrium Calculations 6.E: Equilibrium Chemistry (Exercises) 6.S: Equilibrium Chemistry (Summary) 7: Collecting and Preparing Samples When we use an analytical method to solve a problem, there is no guarantee that our results will be accurate or precise. In designing an analytical method we consider potential sources of determinate error and indeterminate error, and take appropriate steps to minimize their effect, such as including reagent blanks and calibrating instruments. Why might a carefully designed analytical method give poor results? One possibility is that we may have failed to account for errors with the sample. 7.1: The Importance of Sampling 7.2: Designing a Sampling Plan 7.3: Implementing the Sampling Plan 7.4: Separating the Analyte from Interferents 1.3.2 https://chem.libretexts.org/@go/page/190264 7.5: General Theory of Separation Efficiency 7.6: Classifying Separation Techniques 7.7: Liquid–Liquid Extractions 7.8: Separation Versus Preconcentration 7.E: Collecting and Preparing Samples (Exercises) 7.S: Collecting and Preparing Samples (Summary) 8: Gravimetric Methods Gravimetry includes all analytical methods in which the analytical signal is a measurement of mass or a change in mass. When you step on a scale after exercising you are making, in a sense, a gravimetric determination of your mass. Mass is the most fundamental of all analytical measurements, and gravimetry is unquestionably our oldest quantitative analytical technique. 8.1: Overview of Gravimetric Methods 8.2: Precipitation Gravimetry 8.3: Volatilization Gravimetry 8.4: Particulate Gravimetry 8.E: Gravimetric Methods (Exercises) 8.S: Gravimetric Methods (Summary) 9: Titrimetric Methods Titrimetry, in which volume serves as the analytical signal, made its first appearance as an analytical method in the early eighteenth century. Titrimetric methods were not well received by the analytical chemists of that era because they could not duplicate the accuracy and precision of a gravimetric analysis. Not surprisingly, few standard texts from the 1700s and 1800s include titrimetric methods of analysis. 9.1: Overview of Titrimetry 9.2: Acid–Base Titrations 9.3: Complexation Titrations 9.4: Redox Titrations 9.5: Precipitation Titrations 9.E: Titrimetric Methods (Exercises) 9.S: Titrimetric Methods (Summary) 10: Spectroscopic Methods "Colorimetry" is one example of a spectroscopic method of analysis. At the end of the nineteenth century, spectroscopy was limited to the absorption, emission, and scattering of visible, ultraviolet, and infrared electromagnetic radiation. Since its introduction, spectroscopy has expanded to include other forms of electromagnetic radiation—such as X-rays, microwaves, and radio waves—and other energetic particles—such as electrons and ions. 10.1: Overview of Spectroscopy 10.2: Spectroscopy Based on Absorption 10.3: UV/Vis and IR Spectroscopy 10.4: Atomic Absorption Spectroscopy 10.5: Emission Spectroscopy 10.6: Photoluminescence Spectroscopy 10.7: Atomic Emission Spectroscopy 10.8: Spectroscopy Based on Scattering 10.E: Spectroscopic Methods (Exercises) 10.S: Spectroscopic Methods (Summary) 1.3.3 https://chem.libretexts.org/@go/page/190264 11: Electrochemical Methods In Chapter 10 we examined several spectroscopic techniques that take advantage of the interaction between electromagnetic radiation and matter. In this chapter we turn our attention to electrochemical techniques in which the potential, current, or charge in an electrochemical cell serves as the analytical signal. Although there are only three basic electrochemical signals, there are a many possible experimental designs—too many, in fact, to cover adequately in an introductory textbook. 11.1: Overview of Electrochemistry 11.2: Potentiometric Methods 11.3: Coulometric Methods 11.4: Voltammetric Methods 11.E: Electrochemical Methods (Exercises) 11.S: Electrochemical Methods (Summary) 12: Chromatographic & Electrophoretic Methods For this reason, many analytical procedures include a step to separate the analyte from potential interferents. Although effective, each additional step in an analytical procedure increases the analysis time and introduces uncertainty. In this chapter we consider two analytical techniques that avoid these limitations by combining the separation and analysis: chromatography and electrophoresis. 12.1: Overview of Analytical Separations 12.2: General Theory of Column Chromatography 12.3: Optimizing Chromatographic Separations 12.4: Gas Chromatography 12.5: High-Performance Liquid Chromatography 12.6: Other Forms of Liquid Chromatography 12.7: Electrophoresis 12.E: Chromatographic and Electrophoretic Methods (Exercises) 12.S: Chromatographic and Electrophoretic Methods (Summary) 13: Kinetic Methods One way to classify analytical techniques is by whether the analyte’s concentration is determined by an equilibrium reaction or by the kinetics of a chemical reaction or a physical process. Often analytical methods involve measurements made on systems in which the analyte is always at equilibrium. In this chapter we turn our attention to measurements made under nonequilibrium conditions. 13.1: Kinetic Methods Versus Equilibrium Methods 13.2: Chemical Kinetics 13.3: Radiochemistry 13.4: Flow Injection Analysis 13.E: Kinetic Methods (Exercises) 13.S: Kinetic Methods (Summary) 14: Developing a Standard Method Among the goals of analytical chemistry are improving established methods of analysis, extending existing methods of analysis to new types of samples, and developing new analytical methods. In this chapter we discuss how we develop a standard method, including optimizing the experimental procedure, verifying that the method produces acceptable precision and accuracy in the hands of a single analyst, and validating the method for general use. 14.1: Optimizing the Experimental Procedure 14.2: Verifying the Method 14.3: Validating the Method as a Standard Method 14.4: Using Excel and R for an Analysis of Variance 14.E: Developing a Standard Method (Exercises) 14.S: Developing a Standard Method (Summary) 1.3.4 https://chem.libretexts.org/@go/page/190264 15: Quality Assurance Knowing that a method meets suitable standards is important if we are to have confidence in our results. Even so, using a standard method does not guarantee that the result of an analysis is acceptable. In this chapter we introduce the quality assurance procedures used in industry and government labs for monitoring routine chemical analyses. 15.1: The Analytical Perspective—Revisited 15.2: Quality Control 15.3: Quality Assessment 15.4: Evaluating Quality Assurance Data 15.E: Quality Assurance (Exercises) Additional Resources 1.3.5 https://chem.libretexts.org/@go/page/190264 CHAPTER OVERVIEW 2: Introduction to Analytical Chemistry Chemistry is the study of matter, including its composition and structure, its physical properties, and its reactivity. There are many ways to study chemistry, but, we traditionally divide it into five fields: organic chemistry, inorganic chemistry, biochemistry, physical chemistry, and analytical chemistry. Although this division is historical and, perhaps, arbitrary—as witnessed by current interest in interdisciplinary areas such as bioanalytical chemistry and organometallic chemistry—these five fields remain the simplest division spanning the discipline of chemistry. Topic hierarchy 2.1: What is Analytical Chemistry? 2.2: The Analytical Perspective 2.3: Common Analytical Problems 2.4: Introduction to Analytical Chemistry (Exercises) 2.5: Introduction to Analytical Chemistry (Summary) Thumbnail: Several graduated cylinders of various thickness and heights with white side markings in front of a large beaker. They are all filled about halfway with red or blue chemical compounds. The blue ink is showing signs of Brownian motion when dissolving into water. Image used with permission (CC BY-SA 3.0; Horia Varlan from Bucharest, Romania). Contributors David Harvey (DePauw University) This page titled 2: Introduction to Analytical Chemistry is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 1 2.1: What is Analytical Chemistry? 1.1: What is Analytical Chemistry? This page titled 2.1: What is Analytical Chemistry? is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 2.1.1 https://chem.libretexts.org/@go/page/190266 2.2: The Analytical Perspective 1.2: The Analytical Perspective This page titled 2.2: The Analytical Perspective is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 2.2.1 https://chem.libretexts.org/@go/page/190267 2.3: Common Analytical Problems 1.3: Common Analytical Problems This page titled 2.3: Common Analytical Problems is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 2.3.1 https://chem.libretexts.org/@go/page/190268 2.4: Introduction to Analytical Chemistry (Exercises) 1.E: Introduction to Analytical Chemistry (Exercises) This page titled 2.4: Introduction to Analytical Chemistry (Exercises) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 2.4.1 https://chem.libretexts.org/@go/page/190269 2.5: Introduction to Analytical Chemistry (Summary) 1.S: Introduction to Analytical Chemistry (Summary) This page titled 2.5: Introduction to Analytical Chemistry (Summary) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 2.5.1 https://chem.libretexts.org/@go/page/190270 CHAPTER OVERVIEW 3: Basic Tools of Analytical Chemistry In the chapters that follow we will explore many aspects of analytical chemistry. In the process we will consider important questions such as “How do we treat experimental data?”, “How do we ensure that our results are accurate?”, “How do we obtain a representative sample?”, and “How do we select an appropriate analytical technique?” Before we look more closely at these and other questions, we will first review some basic tools of importance to analytical chemists. 3.1: Measurements in Analytical Chemistry 3.2: Concentration 3.3: Stoichiometric Calculations 3.4: Basic Equipment 3.5: Preparing Solutions 3.6: Spreadsheets and Computational Software 3.7: The Laboratory Notebook 3.8: Basic Tools of Analytical Chemistry (Exercises) 3.9: Basic Tools of Analytical Chemistry (Summary) Thumbnail: A Roberval balance. The pivots of the parallelogram understructure makes it insensitive to load positioning away from center, so improves its accuracy, and ease of use. Image used with permission (CC BY-SA 3.0; Nikodem Nijaki) Contributors David Harvey (DePauw University) This page titled 3: Basic Tools of Analytical Chemistry is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 1 3.1: Measurements in Analytical Chemistry 2.1: Measurements in Analytical Chemistry This page titled 3.1: Measurements in Analytical Chemistry is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 3.1.1 https://chem.libretexts.org/@go/page/190272 3.2: Concentration 2.2: Concentration This page titled 3.2: Concentration is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 3.2.1 https://chem.libretexts.org/@go/page/190273 3.3: Stoichiometric Calculations 2.3: Stoichiometric Calculations This page titled 3.3: Stoichiometric Calculations is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 3.3.1 https://chem.libretexts.org/@go/page/190274 3.4: Basic Equipment 2.4: Basic Equipment This page titled 3.4: Basic Equipment is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 3.4.1 https://chem.libretexts.org/@go/page/190275 3.5: Preparing Solutions 2.5: Preparing Solutions This page titled 3.5: Preparing Solutions is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 3.5.1 https://chem.libretexts.org/@go/page/190276 3.6: Spreadsheets and Computational Software 2.6: Spreadsheets and Computational Software This page titled 3.6: Spreadsheets and Computational Software is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 3.6.1 https://chem.libretexts.org/@go/page/190277 3.7: The Laboratory Notebook 2.7: The Laboratory Notebook This page titled 3.7: The Laboratory Notebook is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 3.7.1 https://chem.libretexts.org/@go/page/190278 3.8: Basic Tools of Analytical Chemistry (Exercises) 2.E: Basic Tools of Analytical Chemistry (Exercises) This page titled 3.8: Basic Tools of Analytical Chemistry (Exercises) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 3.8.1 https://chem.libretexts.org/@go/page/190279 3.9: Basic Tools of Analytical Chemistry (Summary) 2.S: Basic Tools of Analytical Chemistry (Summary) This page titled 3.9: Basic Tools of Analytical Chemistry (Summary) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 3.9.1 https://chem.libretexts.org/@go/page/190280 CHAPTER OVERVIEW 4: The Vocabulary of Analytical Chemistry If you leaf through an issue of the journal Analytical Chemistry, you will soon discover that the authors and readers share a common vocabulary of analytical terms. You are probably familiar with some of these terms, such as accuracy and precision, but other terms, such as analyte and matrix may be less familiar to you. In order to participate in the community of analytical chemists, you must first understand its vocabulary. The goal of this chapter, therefore, is to introduce you to some important analytical terms. Becoming comfortable with these terms will make the material in the chapters that follow easier to read and understand. 4.1: Analysis, Determination, and Measurement 4.2: Techniques, Methods, Procedures, and Protocols 4.3: Classifying Analytical Techniques 4.4: Selecting an Analytical Method 4.5: Developing the Procedure 4.6: Protocols 4.7: The Importance of Analytical Methodology 4.8: The Vocabulary of Analytical Chemistry (Exercises) 4.9: The Vocabulary of Analytical Chemistry (Summary) Thumbnail: Colonies of fecal coliform bacteria from a water supply. Source: Susan Boyer. Photo courtesy of ARS–USDA (www.ars.usda.gov). Fecal coliform counts provide a general measure of the presence of pathogenic organisms in a water supply. For drinking water, the current maximum contaminant level (MCL) for total coliforms, including fecal coliforms is less than 1 colony/100 mL. Municipal water departments must regularly test the water supply and must take action if more than 5% of the samples in any month test positive for coliform bacteria. Contributors David Harvey (DePauw University) This page titled 4: The Vocabulary of Analytical Chemistry is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 1 4.1: Analysis, Determination, and Measurement 3.1: Analysis, Determination, and Measurement This page titled 4.1: Analysis, Determination, and Measurement is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 4.1.1 https://chem.libretexts.org/@go/page/190282 4.2: Techniques, Methods, Procedures, and Protocols 3.2: Techniques, Methods, Procedures, and Protocols This page titled 4.2: Techniques, Methods, Procedures, and Protocols is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 4.2.1 https://chem.libretexts.org/@go/page/190283 4.3: Classifying Analytical Techniques 3.3: Classifying Analytical Techniques This page titled 4.3: Classifying Analytical Techniques is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 4.3.1 https://chem.libretexts.org/@go/page/190284 4.4: Selecting an Analytical Method 3.4: Selecting an Analytical Method This page titled 4.4: Selecting an Analytical Method is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 4.4.1 https://chem.libretexts.org/@go/page/190285 4.5: Developing the Procedure 3.5: Developing the Procedure This page titled 4.5: Developing the Procedure is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 4.5.1 https://chem.libretexts.org/@go/page/190286 4.6: Protocols 3.6: Protocols This page titled 4.6: Protocols is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 4.6.1 https://chem.libretexts.org/@go/page/190287 4.7: The Importance of Analytical Methodology 3.7: The Importance of Analytical Methodology This page titled 4.7: The Importance of Analytical Methodology is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 4.7.1 https://chem.libretexts.org/@go/page/190288 4.8: The Vocabulary of Analytical Chemistry (Exercises) 3.E: The Vocabulary of Analytical Chemistry (Exercises) This page titled 4.8: The Vocabulary of Analytical Chemistry (Exercises) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 4.8.1 https://chem.libretexts.org/@go/page/190289 4.9: The Vocabulary of Analytical Chemistry (Summary) 3.S: The Vocabulary of Analytical Chemistry (Summary) This page titled 4.9: The Vocabulary of Analytical Chemistry (Summary) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 4.9.1 https://chem.libretexts.org/@go/page/190290 CHAPTER OVERVIEW 5: Evaluating Analytical Data When using an analytical method we make three separate evaluations of experimental error. First, before beginning an analysis we evaluate potential sources of errors to ensure that they will not adversely effect our results. Second, during the analysis we monitor our measurements to ensure that errors remain acceptable. Finally, at the end of the analysis we evaluate the quality of the measurements and results, comparing them to our original design criteria. This chapter provides an introduction to sources of error, to evaluating errors in analytical measurements, and to the statistical analysis of data. 5.1: Characterizing Measurements and Results 5.2: Characterizing Experimental Errors 5.3: Propagation of Uncertainty 5.4: The Distribution of Measurements and Results 5.5: Statistical Analysis of Data 5.6: Statistical Methods for Normal Distributions 5.7: Detection Limits 5.8: Using Excel and R to Analyze Data 5.9: Evaluating Analytical Data (Exercises) 5.10: Evaluating Analytical Data (Summary) Thumbnail: The blue vertical line segments represent multiple realizations of a confidence interval for the population mean μ, represented as a red horizontal dashed line; note that some confidence intervals do not contain the population mean, as expected. Image used with permission (Public Domain; Tsyplakov) . Contributors David Harvey (DePauw University) This page titled 5: Evaluating Analytical Data is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 1 5.1: Characterizing Measurements and Results 4.1: Characterizing Measurements and Results This page titled 5.1: Characterizing Measurements and Results is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 5.1.1 https://chem.libretexts.org/@go/page/190292 5.2: Characterizing Experimental Errors 4.2: Characterizing Experimental Errors This page titled 5.2: Characterizing Experimental Errors is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 5.2.1 https://chem.libretexts.org/@go/page/190293 5.3: Propagation of Uncertainty 4.3: Propagation of Uncertainty This page titled 5.3: Propagation of Uncertainty is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 5.3.1 https://chem.libretexts.org/@go/page/190294 5.4: The Distribution of Measurements and Results 4.4: The Distribution of Measurements and Results This page titled 5.4: The Distribution of Measurements and Results is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 5.4.1 https://chem.libretexts.org/@go/page/190295 5.5: Statistical Analysis of Data 4.5: Statistical Analysis of Data This page titled 5.5: Statistical Analysis of Data is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 5.5.1 https://chem.libretexts.org/@go/page/190296 5.6: Statistical Methods for Normal Distributions 4.6: Statistical Methods for Normal Distributions This page titled 5.6: Statistical Methods for Normal Distributions is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 5.6.1 https://chem.libretexts.org/@go/page/190297 5.7: Detection Limits 4.7: Detection Limits This page titled 5.7: Detection Limits is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 5.7.1 https://chem.libretexts.org/@go/page/190298 5.8: Using Excel and R to Analyze Data 4.8: Using Excel and R to Analyze Data This page titled 5.8: Using Excel and R to Analyze Data is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 5.8.1 https://chem.libretexts.org/@go/page/190299 5.9: Evaluating Analytical Data (Exercises) 4.E: Evaluating Analytical Data (Exercises) This page titled 5.9: Evaluating Analytical Data (Exercises) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 5.9.1 https://chem.libretexts.org/@go/page/190300 5.10: Evaluating Analytical Data (Summary) 4.S: Evaluating Analytical Data (Summary) This page titled 5.10: Evaluating Analytical Data (Summary) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 5.10.1 https://chem.libretexts.org/@go/page/190301 CHAPTER OVERVIEW 6: Standardizing Analytical Methods The American Chemical Society’s Committee on Environmental Improvement defines standardization as the process of determining the relationship between the signal and the amount of analyte in a sample.1 In Chapter 3 we defined this relationship as Stotal = k A n A + Sreag or Stotal = k A C A + Sreag (6.1) where S is the signal, n is the moles of analyte, C is the analyte’s concentration, k is the method’s sensitivity for the analyte, and S is the contribution to S from sources other than the sample. To standardize a method we must determine values for k and S . Strategies for accomplishing this are the subject of this chapter. total A reag A A A total reag 6.1: Analytical Standards 6.2: Calibrating the Signal 6.3: Determining the Sensitivity 6.4: Linear Regression and Calibration Curves 6.5: Blank Corrections 6.6: Using Excel and R for a Regression Analysis 6.7: Standardizing Analytical Methods (Exercises) 6.8: Standardizing Analytical Methods (Summary) Thumbnail: Illustration showing the evaluation of a linear regression in which we assume that all uncertainty is the result of indeterminate errors affecting y. The points in blue, yi, are the original data and the points in red, ŷi, are the predicted values from the regression equation, ŷ = b0 + b1x. The smaller the total residual error (equation 5.16), the better the fit of the straight-line to the data Contributors David Harvey (DePauw University) This page titled 6: Standardizing Analytical Methods is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 1 6.1: Analytical Standards 5.1: Analytical Standards This page titled 6.1: Analytical Standards is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 6.1.1 https://chem.libretexts.org/@go/page/190303 6.2: Calibrating the Signal 5.2: Calibrating the Signal This page titled 6.2: Calibrating the Signal is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 6.2.1 https://chem.libretexts.org/@go/page/190304 6.3: Determining the Sensitivity 5.3: Determining the Sensitivity This page titled 6.3: Determining the Sensitivity is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 6.3.1 https://chem.libretexts.org/@go/page/190305 6.4: Linear Regression and Calibration Curves 5.4: Linear Regression and Calibration Curves This page titled 6.4: Linear Regression and Calibration Curves is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 6.4.1 https://chem.libretexts.org/@go/page/190306 6.5: Blank Corrections 5.5: Blank Corrections This page titled 6.5: Blank Corrections is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 6.5.1 https://chem.libretexts.org/@go/page/190307 6.6: Using Excel and R for a Regression Analysis 5.6: Using Excel and R for a Regression Analysis This page titled 6.6: Using Excel and R for a Regression Analysis is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 6.6.1 https://chem.libretexts.org/@go/page/190308 6.7: Standardizing Analytical Methods (Exercises) 5.E: Standardizing Analytical Methods (Exercises) This page titled 6.7: Standardizing Analytical Methods (Exercises) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 6.7.1 https://chem.libretexts.org/@go/page/190309 6.8: Standardizing Analytical Methods (Summary) 5.S: Standardizing Analytical Methods (Summary) This page titled 6.8: Standardizing Analytical Methods (Summary) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 6.8.1 https://chem.libretexts.org/@go/page/190310 CHAPTER OVERVIEW 7: Equilibrium Chemistry Regardless of the problem on which an analytical chemist is working, its solution requires a knowledge of chemistry and the ability to apply that knowledge. For example, an analytical chemist studying the effect of pollution on spruce trees needs to know, or know where to find, the chemical differences between p‑hydroxybenzoic acid and p‑hydroxyacetophenone, two common phenols found in the needles of spruce trees. Your ability to “think as a chemist” is a product of your experience in the classroom and in the laboratory. The material in this text assumes your familiarity with topics from earlier courses. Because of its importance to analytical chemistry, this chapter provides a review of equilibrium chemistry. Much of the material in this chapter should be familiar to you, although some topics—ladder diagrams and activity, for example—afford you with new ways to look at equilibrium chemistry. 7.1: Reversible Reactions and Chemical Equilibria 7.2: Thermodynamics and Equilibrium Chemistry 7.3: Manipulating Equilibrium Constants 7.4: Equilibrium Constants for Chemical Reactions 7.5: Le Châtelier’s Principle 7.6: Ladder Diagrams 7.7: Solving Equilibrium Problems 7.8: Buffer Solutions 7.9: Activity Effects 7.10: Using Excel and R to Solve Equilibrium Problems 7.11: Some Final Thoughts on Equilibrium Calculations 7.12: Equilibrium Chemistry (Exercises) 7.13: Equilibrium Chemistry (Summary) Thumbnail: The N O ⇌ 2N O system at Different Temperatures. Nitrogen dioxide (N O ) gas converts to the colorless gas dinitrogen tetroxide (N O ) at low temperatures, and converts back to N O at higher temperatures. The bottles in this photograph contain equal amounts of gas at different temperatures. Figure used with permission from Wikipedia (CC BY-SA 3.0). 2 (g) 2 2(g) 2 4 2 Contributors David Harvey (DePauw University) This page titled 7: Equilibrium Chemistry is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 1 7.1: Reversible Reactions and Chemical Equilibria 6.01: Reversible Reactions and Chemical Equilibria This page titled 7.1: Reversible Reactions and Chemical Equilibria is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 7.1.1 https://chem.libretexts.org/@go/page/190312 7.2: Thermodynamics and Equilibrium Chemistry 6.02: Thermodynamics and Equilibrium Chemistry This page titled 7.2: Thermodynamics and Equilibrium Chemistry is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 7.2.1 https://chem.libretexts.org/@go/page/190313 7.3: Manipulating Equilibrium Constants 6.03: Manipulating Equilibrium Constants This page titled 7.3: Manipulating Equilibrium Constants is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 7.3.1 https://chem.libretexts.org/@go/page/190314 7.4: Equilibrium Constants for Chemical Reactions 6.04: Equilibrium Constants for Chemical Reactions This page titled 7.4: Equilibrium Constants for Chemical Reactions is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 7.4.1 https://chem.libretexts.org/@go/page/190315 7.5: Le Châtelier’s Principle 6.05: Le Châtelier’s Principle This page titled 7.5: Le Châtelier’s Principle is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 7.5.1 https://chem.libretexts.org/@go/page/190316 7.6: Ladder Diagrams 6.06: Ladder Diagrams This page titled 7.6: Ladder Diagrams is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 7.6.1 https://chem.libretexts.org/@go/page/190317 7.7: Solving Equilibrium Problems 6.07: Solving Equilibrium Problems This page titled 7.7: Solving Equilibrium Problems is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 7.7.1 https://chem.libretexts.org/@go/page/190318 7.8: Buffer Solutions 6.08: Buffer Solutions This page titled 7.8: Buffer Solutions is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 7.8.1 https://chem.libretexts.org/@go/page/190319 7.9: Activity Effects 6.09: Activity Effects This page titled 7.9: Activity Effects is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 7.9.1 https://chem.libretexts.org/@go/page/190320 7.10: Using Excel and R to Solve Equilibrium Problems 6.10: Using Excel and R to Solve Equilibrium Problems This page titled 7.10: Using Excel and R to Solve Equilibrium Problems is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 7.10.1 https://chem.libretexts.org/@go/page/190321 7.11: Some Final Thoughts on Equilibrium Calculations 6.11: Some Final Thoughts on Equilibrium Calculations This page titled 7.11: Some Final Thoughts on Equilibrium Calculations is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 7.11.1 https://chem.libretexts.org/@go/page/190322 7.12: Equilibrium Chemistry (Exercises) 6.E: Equilibrium Chemistry (Exercises) This page titled 7.12: Equilibrium Chemistry (Exercises) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 7.12.1 https://chem.libretexts.org/@go/page/190323 7.13: Equilibrium Chemistry (Summary) 6.S: Equilibrium Chemistry (Summary) This page titled 7.13: Equilibrium Chemistry (Summary) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 7.13.1 https://chem.libretexts.org/@go/page/190324 CHAPTER OVERVIEW 8: Collecting and Preparing Samples When we use an analytical method to solve a problem, there is no guarantee that our results will be accurate or precise. In designing an analytical method we consider potential sources of determinate error and indeterminate error, and take appropriate steps to minimize their effect, such as including reagent blanks and calibrating instruments. Why might a carefully designed analytical method give poor results? One possibility is that we may have failed to account for errors associated with the sample. If we collect the wrong sample, or if we lose analyte while preparing the sample for analysis, then we introduce a determinate source of error. If we fail to collect enough samples, or if we collect samples of the wrong size, then our precision may suffer. In this chapter we consider how collecting samples and preparing them for analysis affects the accuracy and precision of our results. 8.1: The Importance of Sampling 8.2: Designing a Sampling Plan 8.3: Implementing the Sampling Plan 8.4: Separating the Analyte from Interferents 8.5: General Theory of Separation Efficiency 8.6: Classifying Separation Techniques 8.7: Liquid–Liquid Extractions 8.8: Separation Versus Preconcentration 8.9: Collecting and Preparing Samples (Exercises) 8.10: Collecting and Preparing Samples (Summary) Thumbnail: An example of pipettes and microplates manipulated by an anthropomorphic robot (Andrew Alliance). Image used with permission (Cc BY-SA 3.0; Pzucchel). Contributors David Harvey (DePauw University) This page titled 8: Collecting and Preparing Samples is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 1 8.1: The Importance of Sampling 7.1: The Importance of Sampling This page titled 8.1: The Importance of Sampling is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 8.1.1 https://chem.libretexts.org/@go/page/190326 8.2: Designing a Sampling Plan 7.2: Designing a Sampling Plan This page titled 8.2: Designing a Sampling Plan is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 8.2.1 https://chem.libretexts.org/@go/page/190327 8.3: Implementing the Sampling Plan 7.3: Implementing the Sampling Plan This page titled 8.3: Implementing the Sampling Plan is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 8.3.1 https://chem.libretexts.org/@go/page/190328 8.4: Separating the Analyte from Interferents 7.4: Separating the Analyte from Interferents This page titled 8.4: Separating the Analyte from Interferents is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 8.4.1 https://chem.libretexts.org/@go/page/190329 8.5: General Theory of Separation Efficiency 7.5: General Theory of Separation Efficiency This page titled 8.5: General Theory of Separation Efficiency is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 8.5.1 https://chem.libretexts.org/@go/page/190330 8.6: Classifying Separation Techniques 7.6: Classifying Separation Techniques This page titled 8.6: Classifying Separation Techniques is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 8.6.1 https://chem.libretexts.org/@go/page/190331 8.7: Liquid–Liquid Extractions 7.7: Liquid–Liquid Extractions This page titled 8.7: Liquid–Liquid Extractions is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 8.7.1 https://chem.libretexts.org/@go/page/190332 8.8: Separation Versus Preconcentration 7.8: Separation Versus Preconcentration This page titled 8.8: Separation Versus Preconcentration is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 8.8.1 https://chem.libretexts.org/@go/page/190333 8.9: Collecting and Preparing Samples (Exercises) 7.E: Collecting and Preparing Samples (Exercises) This page titled 8.9: Collecting and Preparing Samples (Exercises) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 8.9.1 https://chem.libretexts.org/@go/page/190334 8.10: Collecting and Preparing Samples (Summary) 7.S: Collecting and Preparing Samples (Summary) This page titled 8.10: Collecting and Preparing Samples (Summary) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 8.10.1 https://chem.libretexts.org/@go/page/190335 CHAPTER OVERVIEW 9: Gravimetric Methods Gravimetry includes all analytical methods in which the analytical signal is a measurement of mass or a change in mass. When you step on a scale after exercising you are making, in a sense, a gravimetric determination of your mass. Mass is the most fundamental of all analytical measurements, and gravimetry is unquestionably our oldest quantitative analytical technique. The publication in 1540 of Vannoccio Biringuccio’s Pirotechnia is an early example of applying gravimetry—although not yet known by this name— to the analysis of metals and ores.1 Although gravimetry no longer is the most important analytical method, it continues to find use in specialized applications. 9.1: Overview of Gravimetric Methods 9.2: Precipitation Gravimetry 9.3: Volatilization Gravimetry 9.4: Particulate Gravimetry 9.5: Gravimetric Methods (Exercises) 9.6: Gravimetric Methods (Summary) Thumbnails: An analytical balance (Mettler ae-260) that is often used in gravimetric analysis Methods. Image used with permission (Public Domain; US DEA). Contributors David Harvey (DePauw University) This page titled 9: Gravimetric Methods is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 1 9.1: Overview of Gravimetric Methods 8.1: Overview of Gravimetric Methods This page titled 9.1: Overview of Gravimetric Methods is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 9.1.1 https://chem.libretexts.org/@go/page/190337 9.2: Precipitation Gravimetry 8.2: Precipitation Gravimetry This page titled 9.2: Precipitation Gravimetry is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 9.2.1 https://chem.libretexts.org/@go/page/190338 9.3: Volatilization Gravimetry 8.3: Volatilization Gravimetry This page titled 9.3: Volatilization Gravimetry is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 9.3.1 https://chem.libretexts.org/@go/page/190339 9.4: Particulate Gravimetry 8.4: Particulate Gravimetry This page titled 9.4: Particulate Gravimetry is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 9.4.1 https://chem.libretexts.org/@go/page/190340 9.5: Gravimetric Methods (Exercises) 8.E: Gravimetric Methods (Exercises) This page titled 9.5: Gravimetric Methods (Exercises) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 9.5.1 https://chem.libretexts.org/@go/page/190341 9.6: Gravimetric Methods (Summary) 8.S: Gravimetric Methods (Summary) This page titled 9.6: Gravimetric Methods (Summary) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 9.6.1 https://chem.libretexts.org/@go/page/190342 CHAPTER OVERVIEW 10: Titrimetric Methods Titrimetry, in which volume serves as the analytical signal, made its first appearance as an analytical method in the early eighteenth century. Titrimetric methods were not well received by the analytical chemists of that era because they could not duplicate the accuracy and precision of a gravimetric analysis. Not surprisingly, few standard texts from the 1700s and 1800s include titrimetric methods of analysis. Precipitation gravimetry developed as an analytical method without a general theory of precipitation. An empirical relationship between a precipitate’s mass and the mass of analyte—what analytical chemists call a gravimetric factor—was determined experimentally by taking a known mass of analyte through the procedure. Today, we recognize this as an early example of an external standardization. Gravimetric factors were not calculated using the stoichiometry of a precipitation reaction because chemical formulas and atomic weights were not yet available! Unlike gravimetry, the development and acceptance of titrimetry required a deeper understanding of stoichiometry, of thermodynamics, and of chemical equilibria. By the 1900s, the accuracy and precision of titrimetric methods were comparable to that of gravimetric methods, establishing titrimetry as an accepted analytical technique. 10.1: Overview of Titrimetry 10.2: Acid–Base Titrations 10.3: Complexation Titrations 10.4: Redox Titrations 10.5: Precipitation Titrations 10.6: Titrimetric Methods (Exercises) 10.7: Titrimetric Methods (Summary) Thumbnail: A Winkler titration to determine the concentration of dissolved oxygen in a water sample. The dissolved oxygen has been converted to an equivalent amount of iodine, which is being titrated with thiosulfate using a starch indicator. The blue color in the flask will disappear when all the iodine has been converted to iodide. Image used with permission (CC BY-SA 3.0; Will Woodgate (Cornwall College, UK)). Contributors David Harvey (DePauw University) This page titled 10: Titrimetric Methods is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 1 10.1: Overview of Titrimetry 9.1: Overview of Titrimetry This page titled 10.1: Overview of Titrimetry is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 10.1.1 https://chem.libretexts.org/@go/page/190344 10.2: Acid–Base Titrations 9.2: Acid–Base Titrations This page titled 10.2: Acid–Base Titrations is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 10.2.1 https://chem.libretexts.org/@go/page/190345 10.3: Complexation Titrations 9.3: Complexation Titrations This page titled 10.3: Complexation Titrations is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 10.3.1 https://chem.libretexts.org/@go/page/190346 10.4: Redox Titrations 9.4: Redox Titrations This page titled 10.4: Redox Titrations is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 10.4.1 https://chem.libretexts.org/@go/page/190347 10.5: Precipitation Titrations 9.5: Precipitation Titrations This page titled 10.5: Precipitation Titrations is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 10.5.1 https://chem.libretexts.org/@go/page/190348 10.6: Titrimetric Methods (Exercises) 9.E: Titrimetric Methods (Exercises) This page titled 10.6: Titrimetric Methods (Exercises) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 10.6.1 https://chem.libretexts.org/@go/page/190349 10.7: Titrimetric Methods (Summary) 9.S: Titrimetric Methods (Summary) This page titled 10.7: Titrimetric Methods (Summary) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 10.7.1 https://chem.libretexts.org/@go/page/190350 CHAPTER OVERVIEW 11: Spectroscopic Methods An early example of a colorimetric analysis is Nessler’s method for ammonia, which was introduced in 1856. Nessler found that adding an alkaline solution of HgI2 and KI to a dilute solution of ammonia produces a yellow to reddish brown colloid, with the colloid’s color depending on the concentration of ammonia. By visually comparing the color of a sample to the colors of a series of standards, Nessler was able to determine the concentration of ammonia. Colorimetry, in which a sample absorbs visible light, is one example of a spectroscopic method of analysis. At the end of the nineteenth century, spectroscopy was limited to the absorption, emission, and scattering of visible, ultraviolet, and infrared electromagnetic radiation. Since its introduction, spectroscopy has expanded to include other forms of electromagnetic radiation— such as X-rays, microwaves, and radio waves—and other energetic particles—such as electrons and ions. 11.1: Overview of Spectroscopy 11.2: Spectroscopy Based on Absorption 11.03: UV 11.3: UV/Vis and IR Spectroscopy 11.4: Atomic Absorption Spectroscopy 11.5: Emission Spectroscopy 11.6: Photoluminescence Spectroscopy 11.7: Atomic Emission Spectroscopy 11.8: Spectroscopy Based on Scattering 11.9: Spectroscopic Methods (Exercises) 11.10: Spectroscopic Methods (Summary) Contributors David Harvey (DePauw University) This page titled 11: Spectroscopic Methods is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 1 11.1: Overview of Spectroscopy 10.1: Overview of Spectroscopy This page titled 11.1: Overview of Spectroscopy is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 11.1.1 https://chem.libretexts.org/@go/page/190352 11.2: Spectroscopy Based on Absorption 10.2: Spectroscopy Based on Absorption This page titled 11.2: Spectroscopy Based on Absorption is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 11.2.1 https://chem.libretexts.org/@go/page/190353 11.03: UV This page was auto-generated because a user created a sub-page to this page. 11.03: UV is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts. 11.03.1 https://chem.libretexts.org/@go/page/190354 11.3: UV/Vis and IR Spectroscopy 10.3: UV/Vis and IR Spectroscopy This page titled 11.3: UV/Vis and IR Spectroscopy is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 11.3.1 https://chem.libretexts.org/@go/page/190355 11.4: Atomic Absorption Spectroscopy 10.4: Atomic Absorption Spectroscopy This page titled 11.4: Atomic Absorption Spectroscopy is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 11.4.1 https://chem.libretexts.org/@go/page/190357 11.5: Emission Spectroscopy 10.5: Emission Spectroscopy This page titled 11.5: Emission Spectroscopy is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 11.5.1 https://chem.libretexts.org/@go/page/190358 11.6: Photoluminescence Spectroscopy 10.6: Photoluminescence Spectroscopy This page titled 11.6: Photoluminescence Spectroscopy is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 11.6.1 https://chem.libretexts.org/@go/page/190359 11.7: Atomic Emission Spectroscopy 10.7: Atomic Emission Spectroscopy This page titled 11.7: Atomic Emission Spectroscopy is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 11.7.1 https://chem.libretexts.org/@go/page/190360 11.8: Spectroscopy Based on Scattering 10.8: Spectroscopy Based on Scattering This page titled 11.8: Spectroscopy Based on Scattering is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 11.8.1 https://chem.libretexts.org/@go/page/190361 11.9: Spectroscopic Methods (Exercises) 10.E: Spectroscopic Methods (Exercises) This page titled 11.9: Spectroscopic Methods (Exercises) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 11.9.1 https://chem.libretexts.org/@go/page/190362 11.10: Spectroscopic Methods (Summary) 10.S: Spectroscopic Methods (Summary) This page titled 11.10: Spectroscopic Methods (Summary) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 11.10.1 https://chem.libretexts.org/@go/page/190363 CHAPTER OVERVIEW 12: Electrochemical Methods In Chapter 10 we examined several spectroscopic techniques that take advantage of the interaction between electromagnetic radiation and matter. In this chapter we turn our attention to electrochemical techniques in which the potential, current, or charge in an electrochemical cell serves as the analytical signal. Although there are only three basic electrochemical signals, there are a many possible experimental designs—too many, in fact, to cover adequately in an introductory textbook. The simplest division of electrochemical techniques is between bulk techniques, in which we measure a property of the solution in the electrochemical cell, and interfacial techniques, in which the potential, charge, or current depends on the species present at the interface between an electrode and the solution in which it sits. The measurement of a solution’s conductivity, which is proportional to the total concentration of dissolved ions, is one example of a bulk electrochemical technique. A determination of pH using a pH electrode is an example of an interfacial electrochemical technique. Only interfacial electrochemical methods receive further consideration in this chapter. 12.1: Overview of Electrochemistry 12.2: Potentiometric Methods 12.3: Coulometric Methods 12.4: Voltammetric Methods 12.5: Electrochemical Methods (Exercises) 12.6: Electrochemical Methods (Summary) Thumbnail:Comparison of the current response of a platinum disc electrode in 1 M sulfuric acid given by linear sweep voltammetry and staircase voltammetry methods. Image used with permission (CC BY-SA 3.0; Earth-Rare). Contributors David Harvey (DePauw University) This page titled 12: Electrochemical Methods is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 1 12.1: Overview of Electrochemistry 11.1: Overview of Electrochemistry This page titled 12.1: Overview of Electrochemistry is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 12.1.1 https://chem.libretexts.org/@go/page/190365 12.2: Potentiometric Methods 11.2: Potentiometric Methods This page titled 12.2: Potentiometric Methods is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 12.2.1 https://chem.libretexts.org/@go/page/190366 12.3: Coulometric Methods 11.3: Coulometric Methods This page titled 12.3: Coulometric Methods is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 12.3.1 https://chem.libretexts.org/@go/page/190367 12.4: Voltammetric Methods 11.4: Voltammetric Methods This page titled 12.4: Voltammetric Methods is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 12.4.1 https://chem.libretexts.org/@go/page/190368 12.5: Electrochemical Methods (Exercises) 11.E: Electrochemical Methods (Exercises) This page titled 12.5: Electrochemical Methods (Exercises) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 12.5.1 https://chem.libretexts.org/@go/page/190369 12.6: Electrochemical Methods (Summary) 11.S: Electrochemical Methods (Summary) This page titled 12.6: Electrochemical Methods (Summary) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 12.6.1 https://chem.libretexts.org/@go/page/190370 CHAPTER OVERVIEW 13: Chromatographic Drawing from an arsenal of analytical techniques—many of which were the subject of the preceding four chapters—analytical chemists design methods for the analysis of analytes at increasingly lower concentrations and in increasingly more complex matrices. Despite the power of these analytical techniques, they often suffer from a lack of selectivity. For this reason, many analytical procedures include a step to separate the analyte from potential interferents. Although effective, each additional step in an analytical procedure increases the analysis time and introduces uncertainty. In this chapter we consider two analytical techniques that avoid these limitations by combining the separation and analysis: chromatography and electrophoresis. 13.1: Overview of Analytical Separations 13.2: General Theory of Column Chromatography 13.3: Optimizing Chromatographic Separations 13.4: Gas Chromatography 13.5: High-Performance Liquid Chromatography 13.6: Other Forms of Liquid Chromatography 13.7: Electrophoresis 13.8: Chromatographic and Electrophoretic Methods (Exercises) 13.9: Chromatographic and Electrophoretic Methods (Summary) Thumbnail: Separation of black ink on a thin layer chromatography plate. Image used with permission (CC BY-SA 3.0; Natrij)} Contributors David Harvey (DePauw University) This page titled 13: Chromatographic is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 1 13.1: Overview of Analytical Separations 12.1: Overview of Analytical Separations This page titled 13.1: Overview of Analytical Separations is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 13.1.1 https://chem.libretexts.org/@go/page/190373 13.2: General Theory of Column Chromatography 12.2: General Theory of Column Chromatography This page titled 13.2: General Theory of Column Chromatography is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 13.2.1 https://chem.libretexts.org/@go/page/190374 13.3: Optimizing Chromatographic Separations 12.3: Optimizing Chromatographic Separations This page titled 13.3: Optimizing Chromatographic Separations is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 13.3.1 https://chem.libretexts.org/@go/page/190375 13.4: Gas Chromatography 12.4: Gas Chromatography This page titled 13.4: Gas Chromatography is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 13.4.1 https://chem.libretexts.org/@go/page/190376 13.5: High-Performance Liquid Chromatography 12.5: High-Performance Liquid Chromatography This page titled 13.5: High-Performance Liquid Chromatography is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 13.5.1 https://chem.libretexts.org/@go/page/190377 13.6: Other Forms of Liquid Chromatography 12.6: Other Forms of Liquid Chromatography This page titled 13.6: Other Forms of Liquid Chromatography is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 13.6.1 https://chem.libretexts.org/@go/page/190378 13.7: Electrophoresis 12.7: Electrophoresis This page titled 13.7: Electrophoresis is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 13.7.1 https://chem.libretexts.org/@go/page/190379 13.8: Chromatographic and Electrophoretic Methods (Exercises) 12.E: Chromatographic and Electrophoretic Methods (Exercises) Page ID 190380 This page titled 13.8: Chromatographic and Electrophoretic Methods (Exercises) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 13.8.1 https://chem.libretexts.org/@go/page/190380 13.9: Chromatographic and Electrophoretic Methods (Summary) 12.S: Chromatographic and Electrophoretic Methods (Summary) This page titled 13.9: Chromatographic and Electrophoretic Methods (Summary) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 13.9.1 https://chem.libretexts.org/@go/page/190381 CHAPTER OVERVIEW 14: Kinetic Methods There are many ways to categorize analytical techniques, several of which we introduced in earlier chapters. In Chapter 3 we classified techniques by whether the signal is proportional to the absolute amount or the relative amount of analyte. For example, precipitation gravimetry is a total analysis technique because the precipitate’s mass is proportional to the absolute amount, or moles, of analyte. UV/Vis absorption spectroscopy, on the other hand, is a concentration technique because absorbance is proportional to the relative amount, or concentration, of analyte. A second method for classifying analytical techniques is to consider the source of the analytical signal. For example, gravimetry encompasses all techniques in which the analytical signal is a measurement of mass or a change in mass. Spectroscopy, on the other hand, includes those techniques in which we probe a sample with an energetic particle, such as the absorption of a photon. This is the classification scheme used in organizing Chapters 8–11. Another way to classify analytical techniques is by whether the analyte’s concentration is determined by an equilibrium reaction or by the kinetics of a chemical reaction or a physical process. The analytical methods described in Chapter 8–11 mostly involve measurements made on systems in which the analyte is always at equilibrium. In this chapter we turn our attention to measurements made under non-equilibrium conditions. 14.1: Kinetic Methods Versus Equilibrium Methods 14.2: Chemical Kinetics 14.3: Radiochemistry 14.4: Flow Injection Analysis 14.5: Kinetic Methods (Exercises) 14.6: Kinetic Methods (Summary) Thumbnail: Determination of a reaction’s intermediate rate from the slope of a line tangent to a curve showing the change in the analyte’s concentration as a function of time. Contributors David Harvey (DePauw University) This page titled 14: Kinetic Methods is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 1 14.1: Kinetic Methods Versus Equilibrium Methods 13.1: Kinetic Methods Versus Equilibrium Methods This page titled 14.1: Kinetic Methods Versus Equilibrium Methods is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 14.1.1 https://chem.libretexts.org/@go/page/190383 14.2: Chemical Kinetics 13.2: Chemical Kinetics This page titled 14.2: Chemical Kinetics is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 14.2.1 https://chem.libretexts.org/@go/page/190384 14.3: Radiochemistry 13.3: Radiochemistry This page titled 14.3: Radiochemistry is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 14.3.1 https://chem.libretexts.org/@go/page/190385 14.4: Flow Injection Analysis 13.4: Flow Injection Analysis This page titled 14.4: Flow Injection Analysis is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 14.4.1 https://chem.libretexts.org/@go/page/190386 14.5: Kinetic Methods (Exercises) 13.E: Kinetic Methods (Exercises) This page titled 14.5: Kinetic Methods (Exercises) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 14.5.1 https://chem.libretexts.org/@go/page/190387 14.6: Kinetic Methods (Summary) 13.S: Kinetic Methods (Summary) This page titled 14.6: Kinetic Methods (Summary) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 14.6.1 https://chem.libretexts.org/@go/page/190388 CHAPTER OVERVIEW 15: Developing a Standard Method In Chapter 1 we made a distinction between analytical chemistry and chemical analysis. Among the goals of analytical chemistry are improving established methods of analysis, extending existing methods of analysis to new types of samples, and developing new analytical methods. Once we develop a new method, its routine application is best described as chemical analysis. We recognize the status of these methods by calling them standard methods. Numerous examples of standard methods are presented and discussed in Chapters 8–13. What we have not yet considered is what constitutes a standard method. In this chapter we discuss how we develop a standard method, including optimizing the experimental procedure, verifying that the method produces acceptable precision and accuracy in the hands of a single analyst, and validating the method for general use. 15.1: Optimizing the Experimental Procedure 15.2: Verifying the Method 15.3: Validating the Method as a Standard Method 15.4: Using Excel and R for an Analysis of Variance 15.5: Developing a Standard Method (Exercises) 15.6: Developing a Standard Method (Summary) Contributors David Harvey (DePauw University) This page titled 15: Developing a Standard Method is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 1 15.1: Optimizing the Experimental Procedure 14.1: Optimizing the Experimental Procedure This page titled 15.1: Optimizing the Experimental Procedure is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 15.1.1 https://chem.libretexts.org/@go/page/190390 15.2: Verifying the Method 14.2: Verifying the Method This page titled 15.2: Verifying the Method is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 15.2.1 https://chem.libretexts.org/@go/page/190391 15.3: Validating the Method as a Standard Method 14.3: Validating the Method as a Standard Method This page titled 15.3: Validating the Method as a Standard Method is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 15.3.1 https://chem.libretexts.org/@go/page/190392 15.4: Using Excel and R for an Analysis of Variance 14.4: Using Excel and R for an Analysis of Variance This page titled 15.4: Using Excel and R for an Analysis of Variance is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 15.4.1 https://chem.libretexts.org/@go/page/190393 15.5: Developing a Standard Method (Exercises) 14.E: Developing a Standard Method (Exercises) This page titled 15.5: Developing a Standard Method (Exercises) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 15.5.1 https://chem.libretexts.org/@go/page/190394 15.6: Developing a Standard Method (Summary) 14.S: Developing a Standard Method (Summary) This page titled 15.6: Developing a Standard Method (Summary) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 15.6.1 https://chem.libretexts.org/@go/page/190395 CHAPTER OVERVIEW 16: Quality Assurance In Chapter 14 we discussed the process of developing a standard method, including optimizing the experimental procedure, verifying that the method produces acceptable precision and accuracy in the hands of a signal analyst, and validating the method for general use by the broader analytical community. Knowing that a method meets suitable standards is important if we are to have confidence in our results. Even so, using a standard method does not guarantee that the result of an analysis is acceptable. In this chapter we introduce the quality assurance procedures used in industry and government labs for monitoring routine chemical analyses. 16.1: The Analytical Perspective—Revisited 16.2: Quality Control 16.3: Quality Assessment 16.4: Evaluating Quality Assurance Data 16.5: Quality Assurance (Exercises) Thumbnail: Examples of property control charts that show a sequence of results. Contributors David Harvey (DePauw University) This page titled 16: Quality Assurance is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 1 16.1: The Analytical Perspective—Revisited 15.1: The Analytical Perspective—Revisited This page titled 16.1: The Analytical Perspective—Revisited is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 16.1.1 https://chem.libretexts.org/@go/page/190397 16.2: Quality Control 15.2: Quality Control This page titled 16.2: Quality Control is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 16.2.1 https://chem.libretexts.org/@go/page/190398 16.3: Quality Assessment 15.3: Quality Assessment This page titled 16.3: Quality Assessment is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 16.3.1 https://chem.libretexts.org/@go/page/190399 16.4: Evaluating Quality Assurance Data 15.4: Evaluating Quality Assurance Data This page titled 16.4: Evaluating Quality Assurance Data is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 16.4.1 https://chem.libretexts.org/@go/page/190400 16.5: Quality Assurance (Exercises) 15.E: Quality Assurance (Exercises) This page titled 16.5: Quality Assurance (Exercises) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 16.5.1 https://chem.libretexts.org/@go/page/190401 17: Additional Resources Gathered here are three types of resources: suggested experiments, mostly from the Journal of Chemical Education and The Chemical Educator, that provide practical examples of concepts in the textbook; additional readings from the analytical literature that extend and supplement topics covered in the textbook; and electronic resources, many of which are cataloged in the Analytical Sciences Digital Library, that help illustrate concepts from the textbook. Although primarily intended for the use of instructors, these resources also will benefit students who wish to pursue a topic at more depth. The following experiments provide useful introductions to the statistical analysis of data in the analytical chemistry laboratory. Bularzik, J. “The Penny Experiment Revisited: An Illustration of Significant Figures, Accuracy, Precision, and Data Analysis,” J. Chem. Educ. 2007, 84, 1456–1458. Columbia, M. R. “The Statistics of Coffee: 1. Evaluation of Trace Metals for Establishing a Coffee’s Country of Origin Based on a Means Comparison,” Chem. Educator 2007, 12, 260–262. Cunningham, C. C.; Brown, G. R.; St Pierre, L. E. “Evaluation of Experimental Data,” J. Chem. Educ. 1981, 58, 509–511. Edminston, P. L.; Williams, T. R. “An Analytical Laboratory Experiment in Error Analysis: Repeated Determination of Glucose Using Commercial Glucometers,” J. Chem. Educ. 2000, 77, 377–379. Gordus, A. A. “Statistical Evaluation of Class Data for Two Buret Readings,” J. Chem. Educ. 1987, 64, 376–377. Harvey, D. T. “Statistical Evaluation of Acid/Base Indicators,” J. Chem. Educ. 1991, 68, 329–331. Hibbert, D. B. “Teaching modern data analysis with The Royal Austrian Chemical Institute’s titration competition,” Aust. J. Ed. Chem. 2006, 66, 5–11. Johll, M. E.; Poister, D.; Ferguson, J. “Statistical Comparison of Multiple Methods for the Determination of Dissolved Oxygen Levels in Natural Water,” Chem. Educator 2002, 7, 146–148. Jordon, A. D. “Which Method is Most Precise; Which is Most Accurate?,” J. Chem. Educ. 2007, 84, 1459–1460. Olsen, R. J. “Using Pooled Data and Data Visualization To Introduce Statistical Concepts in the General Chemistry Laboratory,” J. Chem. Educ. 2008, 85, 544–545. O’Reilley, J. E. “The Length of a Pestle,” J. Chem. Educ. 1986, 63, 894–896. Paselk, R. A. “An Experiment for Introducing Statistics to Students of Analytical and Clinical Chemistry,” J. Chem. Educ. 1985, 62, 536. Puignou, L.; Llauradó, M. “An Experimental Introduction to Interlaboratory Exercises in Analytical Chemistry,” J. Chem. Educ. 2005, 82, 1079–1081. Quintar, S. E.; Santagata, J. P.; Villegas, O. I.; Cortinez, V. A. “Detection of Method Effects on Quality of Analytical Data,” J. Chem. Educ. 2003, 80, 326–329. Richardson, T. H. “Reproducible Bad Data for Instruction in Statistical Methods,” J. Chem. Educ. 1991, 68, 310–311. Salzsieder, J. C. “Statistical Analysis Experiment for Freshman Chemistry Lab,” J. Chem. Educ. 1995, 72, 623. Samide, M. J. “Statistical Comparison of Data in the Analytical Laboratory,” J. Chem. Educ. 2004, 81, 1641–1643. Sheeran, D. “Copper Content in Synthetic Copper Carbonate: A Statistical Comparison of Experimental and Expected Results,” J. Chem. Educ. 1998, 75, 453–456. Spencer, R. D. “The Dependence of Strength in Plastics upon Polymer Chain Length and Chain Orientation,” J. Chem. Educ. 1984, 61, 555–563. Stolzberg, R. J. “Do New Pennies Lose Their Shells? Hypothesis Testing in the Sophomore Analytical Chemistry Laboratory,” J. Chem. Educ. 1998, 75, 1453–1455. Stone, C. A.; Mumaw, L. D. “Practical Experiments in Statistics,” J. Chem. Educ. 1995, 72, 518–524. Thomasson, K.; Lofthus-Merschman, S.; Humbert, M.; Kulevsky, N. “Applying Statistics in the Undergraduate Chemistry Laboratory: Experiments with Food Dyes,” J. Chem. Educ. 1998, 75, 231–233. Vitha, M. F.; Carr, P. W. “A Laboratory Exercise in Statistical Analysis of Data,” J. Chem. Educ. 1997, 74, 998–1000. A more comprehensive discussion of the analysis of data, covering all topics considered in this chapter as well as additional material, can be found in any textbook on statistics or data analysis; several such texts are listed here. Anderson, R. L. Practical Statistics for Analytical Chemists, Van Nostrand Reinhold: New York; 1987. Graham, R. C. Data Analysis for the Chemical Sciences, VCH Publishers: New York; 1993. Mark, H.; Workman, J. Statistics in Spectroscopy, Academic Press: Boston; 1991. 17.1 https://chem.libretexts.org/@go/page/190402 Mason, R. L.; Gunst, R. F.; Hess, J. L. Statistical Design and Analysis of Experiments; Wiley: New York, 1989. Massart, D. L.; Vandeginste, B. G. M.; Buydens, L. M. C.; De Jong, S.; Lewi, P. J.; Smeyers-Verbeke, J. Handbook of Chemometrics and Qualimetrics, Elsevier: Amsterdam, 1997. Miller, J. C.; Miller, J. N. Statistics for Analytical Chemistry, Ellis Horwood PTR Prentice-Hall: New York; 3rd Edition, 1993. NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/, 2006. Sharaf, M. H.; Illman, D. L.; Kowalski, B. R. Chemometrics, Wiley-Interscience: New York; 1986. The importance of defining statistical terms is covered in the following papers. Analytical Methods Committee “Terminology—the key to understanding analytical science. Part 1: Accuracy, precision and uncertainty,” AMC Technical Brief No. 13, Sept. 2003 (http://www.rsc.org/lap/rsccom/amc/amc_index.htm). Goedart, M. J.; Verdonk, A. H. “The Development of Statistical Concepts in a Design-Oriented Laboratory Course in Scientific Measuring,” J. Chem. Educ. 1991, 68, 1005–1009. Sánchez, J. M. “Teaching Basic Applied Statistics in University Chemistry Courses: Students’ Misconceptions,” Chem. Educator 2006, 11, 1–4. Thompson, M. “Towards a unified model of errors in analytical measurements,” Analyst 2000, 125, 2020–2025. Treptow, R. S. “Precision and Accuracy in Measurements,” J. Chem. Educ. 1998, 75, 992–995. The detection of outliers, particularly when working with a small number of samples, is discussed in the following papers. Analytical Methods Committee “Robust Statistics—How Not To Reject Outliers Part 1. Basic Concepts,” Analyst 1989, 114, 1693–1697. Analytical Methods Committee “Robust Statistics—How Not to Reject Outliers Part 2. Inter-laboratory Trials,” Analyst 1989, 114, 1699–1702. Analytical Methods Committee “Robust statistics: a method of coping with outliers,” AMC Technical Brief No. 6, April 2001 (http://www.rsc.org/lap/rsccom/amc/amc_index.htm). Efstathiou, C. “Stochastic Calculation of Critical Q-Test Values for the Detection of Outliers in Measurements,” J. Chem. Educ. 1992, 69, 773–736. Efstathiou, C. “Estimation of type 1 error probability from experimental Dixon’s Q parameter on testing for outliers within small data sets,” Talanta 2006, 69, 1068–1071. Kelly, P. C. “Outlier Detection in Collaborative Studies,” Anal. Chem. 1990, 73, 58–64. Mitschele, J. “Small Sample Statistics,” J. Chem. Educ. 1991, 68, 470–473. The following papers provide additional information on error and uncertainty, including the propagation of uncertainty. Andraos, J. “On the Propagation of Statistical Errors for a Function of Several Variables,” J. Chem. Educ. 1996, 73, 150–154. Donato, H.; Metz, C. “A Direct Method for the Propagation of Error Using a Personal Computer Spreadsheet Program,” J. Chem. Educ. 1988, 65, 867–868. Gordon, R.; Pickering, M.; Bisson, D. “Uncertainty Analysis by the ‘Worst Case’ Method,” J. Chem. Educ. 1984, 61, 780–781. Guare, C. J. “Error, Precision and Uncertainty,” J. Chem. Educ. 1991, 68, 649–652. Guedens, W. J.; Yperman, J.; Mullens, J.; Van Poucke, L. C.; Pauwels, E. J. “Statistical Analysis of Errors: A Practical Approach for an Undergraduate Chemistry Lab Part 1. The Concept,” J. Chem. Educ. 1993, 70, 776–779 Guedens, W. J.; Yperman, J.; Mullens, J.; Van Poucke, L. C.; Pauwels, E. J. “Statistical Analysis of Errors: A Practical Approach for an Undergraduate Chemistry Lab Part 2. Some Worked Examples,” J. Chem. Educ. 1993, 70, 838–841. Heydorn, K. “Detecting Errors in Micro and Trace Analysis by Using Statistics,” Anal. Chim. Acta 1993, 283, 494–499. Hund, E.; Massart, D. L.; Smeyers-Verbeke, J. “Operational definitions of uncertainty,” Trends Anal. Chem. 2001, 20, 394–406. Kragten, J. “Calculating Standard Deviations and Confidence Intervals with a Universally Applicable Spreadsheet Technique,” Analyst 1994, 119, 2161–2165. Taylor, B. N.; Kuyatt, C. E. “Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results,” NIST Technical Note 1297, 1994. Yates, P. C. “A Simple Method for Illustrating Uncertainty Analysis,” J. Chem. Educ. 2001, 78, 770–771. Consult the following resources for a further discussion of detection limits. Boumans, P. W. J. M. “Detection Limits and Spectral Interferences in Atomic Emission Spectrometry,” Anal. Chem. 1984, 66, 459A–467A. 17.2 https://chem.libretexts.org/@go/page/190402 Currie, L. A. “Limits for Qualitative Detection and Quantitative Determination: Application to Radiochemistry,” Anal. Chem. 1968, 40, 586–593. Currie, L. A. (ed.) Detection in Analytical Chemistry: Importance, Theory and Practice, American Chemical Society: Washington, D. C., 1988. Ferrus, R.; Egea, M. R. “Limit of discrimination, limit of detection and sensitivity in analytical systems,” Anal. Chim. Acta 1994, 287, 119–145. Glaser, J. A.; Foerst, D. L.; McKee, G. D.; Quave, S. A.; Budde, W. L. “Trace analyses for wastewaters,” Environ. Sci. Technol. 1981, 15, 1426–1435. Kimbrough, D. E.; Wakakuwa, J. “Quality Control Level: An Introduction to Detection Levels,” Environ. Sci. Technol. 1994, 28, 338–345. The following resources provide additional information on using Excel, including reports of errors in its handling of some statistical procedures. McCollough, B. D.; Wilson, B. “On the accuracy of statistical procedures in Microsoft Excel 2000 and Excel XP,” Comput. Statist. Data Anal. 2002, 40, 713–721. Morgon, S. L.; Deming, S. N. “Guide to Microsoft Excel for calculations, statistics, and plotting data,” (http://www.chem.sc.edu/faculty/morgan/resources/Excel/Excel_Guide_Morgan.pdf). Pottel, H. “Statistical flaws in Excel,” (http://www.coventry.ac.uk/ec/~nhunt/pottel.pdf). To learn more about using R, consult the following resources. Chambers, J. M. Software for Data Analysis: Programming with R, Springer: New York, 2008. Maindonald, J.; Braun, J. Data Analysis and Graphics Using R, Cambridge University Press: Cambridge, UK, 2003. Sarkar, D. Lattice: Multivariate Data Visualization With R, Springer: New York, 2008. The following papers provide insight into visualizing data. Analytical Methods Committee “Representing data distributions with kernel density estimates,” AMC Technical Brief, March 2006 (http://www.rsc.org/lap/rsccom/amc/amc_index.htm). Frigge, M.; Hoaglin, D. C.; Iglewicz, B. “Some Implementations of the Boxplot,” The American Statistician 1989, 43, 50–54. Gathered here are links to on-line computational tools, simulations, and tutorials, many of which are found on the Analytical Sciences Digital Library. Applets for Statistics (link). GraphPad QuickCalcs: Free On-Line Calculators (link). Introduction to Data Analysis (link). Introduction to Probability and Statistics (link). Overway, K. “Population versus Sampling Statistics: A Spreadsheet Exercise,” J. Chem. Educ. 2008 85, 749 (link). Van Bramer, S. E. “A Brief Introduction to the Gaussian Distribution, Sample Statistics, and the Student’s t Statistic,” J. Chem. Educ. 2007, 84, 1231 (link). Web Tutorials in Chemistry—Statistics (link). Chapter 5 Although there are many experiments in the literature that incorporate external standards, the method of standard additions, or internal standards, the issue of choosing a method standardization is not the experiment’s focus. One experiment designed to consider the issue of selecting a method of standardization is given here. Harvey, D. T. “External Standards or Standard Additions? Selecting and Validating a Method of Standardization,” J. Chem. Educ. 2002, 79, 613–615. In addition to the texts listed as suggested readings in Chapter 4, the following text provide additional details on linear regression. Draper, N. R.; Smith, H. Applied Regression Analysis, 2nd. ed.; Wiley: New York, 1981. The following articles providing more details about linear regression. Analytical Methods Committee “Is my calibration linear?” AMC Technical Brief, December 2005 (http://www.rsc.org/pdf/amc/brief3.pdf). 17.3 https://chem.libretexts.org/@go/page/190402 Badertscher, M.; Pretsch, E. “Bad results from good data,” Trends Anal. Chem. 2006, 25, 1131–1138. Boqué, R.; Rius, F. X.; Massart, D. L. “Straight Line Calibration: Something More Than Slopes, In• tercepts, and Correlation Coefficients,” J. Chem. Educ. 1993, 70, 230–232. Danzer, K.; Currie, L. A. “Guidelines for Calibration in Analytical Chemistry. Part 1. Fundamentals and Single Component Calibration,” Pure Appl. Chem. 1998, 70, 993–1014. Henderson, G. “Lecture Graphic Aids for Least-Squares Analysis,” J. Chem. Educ. 1988, 65, 1001–1003. Logan, S. R. “How to Determine the Best Straight Line,” J. Chem. Educ. 1995, 72, 896–898. Miller, J. N. “Basic Statistical Methods for Analytical Chemistry. Part 2. Calibration and Regression Methods,” Analyst 1991, 116, 3–14. Renman, L., Jagner, D. “Asymmetric Distribution of Results in Calibration Curve and Standard Addition Evaluations,” Anal. Chim. Acta 1997, 357, 157–166. Rodriguez, L. C.; Gamiz-Gracia; Almansa-Lopez, E. M.; Bosque-Sendra, J. M. “Calibration in chemical measurement processes. II. A methodological approach,” Trends Anal. Chem. 2001, 20, 620–636. Useful papers providing additional details on the method of standard additions are gathered here. Bader, M. “A Systematic Approach to Standard Addition Methods in Instrumental Analysis,” J. Chem. Educ. 1980, 57, 703– 706. Brown, R. J. C.; Roberts, M. R.; Milton, M. J. T. “Systematic error arising form ‘Sequential’ Standard Addition Calibrations. 2. Determination of Analyte Mass Fraction in Blank Solutions,” Anal. Chim. Acta 2009, 648, 153–156. Brown, R. J. C.; Roberts, M. R.; Milton, M. J. T. “Systematic error arising form ‘Sequential’ Standard Addition Calibrations: Quantification and correction,” Anal. Chim. Acta 2007, 587, 158–163. Bruce, G. R.; Gill, P. S. “Estimates of Precision in a Standard Additions Analysis,” J. Chem. Educ. 1999, 76, 805–807. Kelly, W. R.; MacDonald, B. S.; Guthrie “Gravimetric Approach to the Standard Addition Method in Instrumental Analysis. 1.” Anal. Chem. 2008, 80, 6154–6158. Nimura, Y.; Carr, M. R. “Reduction of the Relative Error in the Standard Additions Method,” Analyst 1990, 115, 1589–1595. The following papers discusses the importance of weighting experimental data when use linear regression. Analytical Methods Committee “Why are we weighting?” AMC Technical Brief, June 2007 (http://www.rsc.org/images/brief27_tcm18-92066.pdf) Karolczak, M. “To Weight or Not to Weight? An Analyst’s Dilemma,” Current Separations 1995, 13, 98–104. Algorithms for performing a linear regression with errors in both X and Y are discussed in the following papers. Also included here are papers that address the difficulty of using linear regression to compare two analytical methods. Irvin, J. A.; Quickenden, T. L. “Linear Least Squares Treatment When There are Errors in Both x and y,” J. Chem. Educ. 1983, 60, 711–712. Kalantar, A. H. “Kerrich’s Method for y = αx Data When Both y and x Are Uncertain,” J. Chem. Educ. 1991, 68, 368–370. Macdonald, J. R.; Thompson, W. J. “Least-Squares Fitting When Both Variables Contain Errors: Pitfalls and Possibilities,” Am. J. Phys. 1992, 60, 66–73. Martin, R. F. “General Deming Regression for Estimating Systematic Bias and Its Confidence Interval in Method-Comparison Studies,” Clin. Chem. 2000, 46, 100–104. Ogren, P. J.; Norton, J. R. “Applying a Simple Linear Least-Squares Algorithm to Data with Uncertainties in Both Variables,” J. Chem. Educ. 1992, 69, A130–A131. Ripley, B. D.; Thompson, M. “Regression Techniques for the Detection of Analytical Bias,” Analyst 1987, 112, 377–383. Outliers present a problem for a linear regression analysis. The following papers discuss the use of robust linear regression techniques. Glaister, P. “Robust Linear Regression Using Thiel’s Method,” J. Chem. Educ. 2005, 82, 1472–1473. Glasser, L. “Dealing with Outliers: Robust, Resistant Regression,” J. Chem. Educ. 2007, 84, 533–534. Ortiz, M. C.; Sarabia, L. A.; Herrero, A. “Robust regression techniques. A useful alternative for the detection of outlier data in chemical analysis,” Talanta 2006, 70, 499–512. The following papers discusses some of the problems with using linear regression to analyze data that has been mathematically transformed into a linear form, as well as alternative methods of evaluating curvilinear data. 17.4 https://chem.libretexts.org/@go/page/190402 Chong, D. P. “On the Use of Least Squares to Fit Data in Linear Form,” J. Chem. Educ. 1994, 71, 489–490. Hinshaw, J. V. “Nonlinear Calibration,” LCGC 2002, 20, 350–355. Lieb, S. G. “Simplex Method of Nonlinear Least-Squares - A Logical Complementary Method to Linear Least-Squares Analysis of Data,” J. Chem. Educ. 1997, 74, 1008–1011. Zielinski, T. J.; Allendoerfer, R. D. “Least Squares Fitting of Nonlinear Data in the Undergraduate Laboratory,” J. Chem. Educ. 1997, 74, 1001–1007. More information on multivariate and multiple regression can be found in the following papers. Danzer, K.; Otto, M.; Currie, L. A. “Guidelines for Calibration in Analytical Chemistry. Part 2. Multispecies Calibration,” Pure Appl. Chem. 2004, 76, 1215–1225. Escandar, G. M.; Faber, N. M.; Goicoechea, H. C.; de la Pena, A. M.; Olivieri, A.; Poppi, R. J. “Second- and third-order multivariate calibration: data, algorithms and applications,” Trends Anal. Chem. 2007, 26, 752–765. Kowalski, B. R.; Seasholtz, M. B. “Recent Developments in Multivariate Calibration,” J. Chemometrics 1991, 5, 129–145. Lang, P. M.; Kalivas, J. H. “A Global Perspective on Multivariate Calibration Methods,” J. Chemometrics 1993, 7, 153–164. Madden, S. P.; Wilson, W.; Dong, A.; Geiger, L.; Mecklin, C. J. “Multiple Linear Regression Using a Graphing Calculator,” J. Chem. Educ. 2004, 81, 903–907. Olivieri, A. C.; Faber, N. M.; Ferré, J.; Boqué, R.; Kalivas, J. H.; Mark, H. “Uncertainty Estimation and Figures of Merit for Multivariate Calibration,” Pure Appl. Chem. 2006, 78, 633–661. An additional discussion on method blanks, including the use of the total Youden blank, is found in the following papers. Cardone, M. J. “Detection and Determination of Error in Analytical Methodology. Part II. Correction for Corrigible Systematic Error in the Course of Real Sample Analysis,” J. Assoc. Off. Anal. Chem. 1983, 66, 1283–1294. Cardone, M. J. “Detection and Determination of Error in Analytical Methodology. Part IIB. Direct Calculational Technique for Making Corrigible Systematic Error Corrections,” J. Assoc. Off. Anal. Chem. 1985, 68, 199-202. Ferrus, R.; Torrades, F. “Bias-Free Adjustment of Analytical Methods to Laboratory Samples in Routine Analytical Procedures,” Anal. Chem. 1988, 60, 1281–1285. Vitha, M. F.; Carr, P. W.; Mabbott, G. A. “Appropriate Use of Blanks, Standards, and Controls in Chemical Measurements,” J. Chem. Educ. 2005, 82, 901–902. There are a variety of computational packages for completing linear regression analyses. These papers provide details on there use in a variety of contexts. Espinosa-Mansilla, A.; de la Peña, A. M.; González-Gómez, D. “Using Univariate Linear Regression Calibration Software in the MATLAB Environment. Application to Chemistry Laboratory Practices,” Chem. Educator 2005, 10, 1–9. Harris, D. C. “Nonlinear Least-Squares Curve Fitting with Microsoft Excel Solver,” J. Chem. Educ. 1998, 75, 119–121. Kim, M. S.; Bukart, M.; Kim, M. H. “A Method Visual Interactive Regression,” J. Chem. Educ. 2006, 83, 1884. Machuca-Herrera, J. G. “Nonlinear Curve Fitting with Spreadsheets,” J. Chem. Educ. 1997, 74, 448–449. Smith, E. T.; Belogay, E. A.; Hõim “Linear Regression and Error Analysis for Calibration Curves and Standard Additions: An Excel Spreadsheet Exercise for Undergraduates,” Chem. Educator 2010, 15, 100–102. Smith, E. T.; Belogay, E. A.; Hõim “Using Multiple Linear Regression to Analyze Mixtures: An Excel Spreadsheet Exercise for Undergraduates,” Chem. Educator 2010, 15, 103–107. Young, S. H.; Wierzbicki, A. “Mathcad in the Chemistry Curriculum. Linear Least-Squares Regression,” J. Chem. Educ. 2000, 77, 669. Young, S. H.; Wierzbicki, A. “Mathcad in the Chemistry Curriculum. Non-Linear Least-Squares Regression,” J. Chem. Educ. 2000, 77, 669. Gathered here are links to on-line computational tools, simulations, and tutorials, many of which are found on the Analytical Sciences Digital Library. Multiple Regression (link). Non-Parametric Regression with Errors in X and Y (link). Linear Regression Tutorial (link). Modeling Data Tutorial (link). 17.5 https://chem.libretexts.org/@go/page/190402 Chapter 6 The following experiments involve the experimental determination of equilibrium constants, the characterization of buffers, and, in some cases, demonstrate the importance of activity effects. “The Effect of Ionic Strength on an Equilibrium Constant (A Class Study)” in Chemical Principles in Practice, J. A. Bell, Ed., Addison-Wesley: Reading, MA, 1967. “Equilibrium Constants for Calcium Iodate Solubility and Iodic Acid Dissociation” in Chemical Principles in Practice, J. A. Bell, Ed., Addison-Wesley: Reading, MA, 1967. “The Solubility of Silver Acetate” in Chemical Principles in Practice, J. A. Bell, Ed., Addison-Wesley: Reading, MA, 1967. Cobb, C. L.; Love, G. A. “Iron(III) Thiocyanate Revisited: A Physical Chemistry Equilibrium Lab Incorporating Ionic Strength Effects,” J. Chem. Educ. 1998, 75, 90–92. Green, D. B.; Rechtsteiner, G.; Honodel, A. “Determination of the Thermodynamic Solubility Product, Ksp, of PbI2 Assuming Nonideal Behavior,” J. Chem. Educ. 1996, 73, 789–792. Russo, S. O.; Hanania, I. H. “Buffer Capacity,” J. Chem. Educ. 1987, 64, 817–819. Stolzberg, R. J. “Discovering a Change in Equilibrium Constant with Change in Ionic Strength,” J. Chem. Educ. 1999, 76, 640– 641. Wiley, J. D. “The Effect of Ionic Strength on the Solubility of an Electrolyte,” J. Chem. Educ. 2004, 81, 1644–1646. A nice discussion of Berthollet’s discovery of the reversibility of reactions is found in Roots-Bernstein, R. S. Discovering, Harvard University Press: Cambridge, MA, 1989. The following texts provide additional coverage of equilibrium chemistry. Butler, J. N. Ionic Equilibria: A Mathematical Approach; Addison-Wesley: Reading, MA, 1964. Butler, J. N. Solubility and pH Calculations; Addison-Wesley: Reading, MA, 1973. Fernando, Q.; Ryan, M. D. Calculations in Analytical Chemistry, Harcourt Brace Jovanovich: New York, 1982. Freiser, H.; Fernando, Q. Ionic Equilibria in Analytical Chemistry, Wiley: New York, 1963. Freiser, H. Concepts and Calculations in Analytical Chemistry, CRC Press: Boca Raton, 1992. Gordus, A. A. Schaum’s Outline of Analytical Chemistry; McGraw-Hill: New York, 1985. Ramette, R. W. Chemical Equilibrium and Analysis, Addison-Wesley: Reading, MA, 1981. The following papers discuss a variety of general aspects of equilibrium chemistry. Gordus, A. A. “Chemical Equilibrium I. The Thermodynamic Equilibrium Concept,” J. Chem. Educ. 1991, 68, 138–140. Gordus, A. A. “Chemical Equilibrium II. Deriving an Exact Equilibrium Equation,” J. Chem. Educ. 1991, 68, 215–217. Gordus, A. A. “Chemical Equilibrium III. A Few Math Tricks,” J. Chem. Educ. 1991, 68, 291–293. Gordus, A. A. “Chemical Equilibrium IV. Weak Acids and Bases,” J. Chem. Educ. 1991, 68, 397–399. Gordus, A. A. “Chemical Equilibrium VI. Buffer Solutions,” J. Chem. Educ. 1991, 68, 656–658. Gordus, A. A. “Chemical Equilibrium VII. Precipitates, “J. Chem. Educ. 1991, 68, 927–930. Thomson, B. M.; Kessick, M. A. “On the Preparation of Buffer Solutions,” J. Chem. Educ. 1981, 58, 743-746. Weltin, E. “Are the Equilibrium Concentrations for a Chemical Reaction Always Uniquely Determined by the Initial Concentrations?” J. Chem. Educ. 1990, 67, 548. Weltin, E. “Are the Equilibrium Compositions Uniquely Determined by the Initial Compositions? Properties of the Gibbs Free Energy Function,” J. Chem. Educ. 1995, 72, 508–511. Collected here are a papers discussing a variety of approaches to solving equilibrium problems. Ault, A. “Do pH in Your Head,” J. Chem. Educ. 1999, 76, 936–938. Chaston, S. “Calculating Complex Equilibrium Concentrations by a Next Guess Factor Method,” J. Chem. Educ. 1993, 70, 622–624. Donato, H. “Graphing Calculator Strategies for Solving Chemical Equilibrium Problems,” J. Chem. Educ. 1999, 76, 632–634. Olivieri, A. C. “Solution of Acid-Base Equilibria by Successive Approximations,” J. Chem. Educ. 1990, 67, 229–231. Weltin, E. “A Numerical Method to Calculate Equilibrium Concentrations for Single-Equation Systems,” J. Chem. Educ. 1991, 68, 486–487. Weltin, E. “Calculating Equilibrium Concentrations,” J. Chem. Educ. 1992, 69, 393–396. 17.6 https://chem.libretexts.org/@go/page/190402 Weltin, E. “Calculating Equilibrium Concentrations for Stepwise Binding of Ligands and Polyprotic Acid-Base Systems,” J. Chem. Educ. 1993, 70, 568–571. Weltin, E. “Equilibrium Calculations are Easier Than You Think - But You do Have to Think!” J. Chem. Educ. 1993, 70, 571– 573. Weltin, E. “Calculating Equilibrium Concentrations by Iteration: Recycle Your Approximations,” J. Chem. Educ. 1995, 72, 36– 38. Additional historical background on the development of the Henderson-Hasselbalch equation is provided by the following papers. de Levie, R. “The Henderson Approximation and the Mass Action Law of Guldberg and Waage,” Chem. Educator 2002, 7, 132–135. de Levie, R. “The Henderson-Hasselbalch Equation: Its History and Limitations,” J. Chem. Educ. 2003, 80, 146. A simulation is a useful tool for helping students gain an intuitive understanding of a topic. Gathered here are some simulations for teaching equilibrium chemistry. Edmonson, L. J.; Lewis, D. L. “Equilibrium Principles: A Game for Students,” J. Chem. Educ. 1999, 76, 502. Huddle, P. A.; White, M. W.; Rogers, F. “Simulations for Teaching Chemical Equilibrium,” J. Chem. Educ. 2000, 77, 920–926. The following papers provide additional resources on ionic strength, activity, and the effect of ionic strength and activity on equilibrium reactions and pH. Clark, R. W.; Bonicamp, J. M. “The Ksp-Solubility Conundrum,” J. Chem. Educ. 1998, 75, 1182–1185. de Levie, R. “On Teaching Ionic Activity Effects: What, When, and Where?” J. Chem. Educ. 2005, 82, 878–884. McCarty, C. G.; Vitz, E. “pH Paradoxes: Demonstrating That It Is Not True That pH = –log[H+],” J. Chem. Educ. 2006, 83, 752–757. Ramshaw, J. D. “Fugacity and Activity in a Nutshell,” J. Chem. Educ. 1995, 72, 601–603. Sastre de Vicente, M. E. “The Concept of Ionic Strength Eighty Years After Its Introduction,” J. Chem. Educ. 2004, 81, 750– 753. Solomon, T. “The Definition and Unit of Ionic Strength,” J. Chem. Educ. 2001, 78, 1691–1692. For a contrarian’s view of equilibrium chemistry, please see the following papers. Hawkes, S. J. “Buffer Calculations Deceive and Obscure,” Chem. Educator, 1996, 1, 1–8. Hawkes, S. J. “What Should We Teach Beginners About Solubility and Solubility Products?” J. Chem. Educ. 1998, 75, 1179– 1181. Hawkes, S. J. “Complexation Calculations are Worse Than Useless,” J. Chem. Educ. 1999, 76, 1099–1100. Hawkes, S. J. “Easy Deviation of pH ≈ (pKa1 + pKa2)/2 Using Autoprotolysis of HA–: Doubtful Value of the Supposedly More Rigorous Equation,” J. Chem. Educ. 2000, 77, 1183–1184. See, also, an exchange of letters between J. J. Roberts and S. J. Hawkes, J. Chem. Educ. 2002, 79, 161–162. Chapter 7 The following set of experiments and class exercises introduce students to the importance of sampling on the quality of analytical results. Bauer, C. F. “Sampling Error Lecture Demonstration,” J. Chem. Educ. 1985, 62, 253. Canaes, L. S.; Brancalion, M. L.; Rossi, A. V.; Rath, S. “Using Candy Samples to Learn About Sampling Techniques and Statistical Evaluation of Data,” J. Chem. Educ. 2008, 85, 1083–1088. Clement, R. E. “Environmental Sampling for Trace Analysis,” Anal. Chem. 1992, 64, 1076A–1081A. Dunn, J. G.; Phillips, D. N.; van Bronswijk, W. “An Exercise to Illustrate the Importance of Sample Preparation in Chemical Analysis,” J. Chem. Educ. 1997, 74, 1188–1191. Fritz, M. D. “A Demonstration of Sample Segregation,” J. Chem. Educ. 2005, 82, 255–256. Guy, R. D.; Ramaley, L.; Wentzell, P. D. “An Experiment in the Sampling of Solids for Chemical Analysis”, J. Chem. Educ. 1998, 75, 1028-1033. Hartman, J. R. “An In-Class Experiment to Illustrate the Importance of Sampling Techniques and Statistical Analysis of Data to Quantitative Analysis Students,” J. Chem. Educ. 2000, 77, 1017–1018. Harvey, D. T. “Two Experiments Illustrating the Importance of Sampling in a Quantitative Chemical Analysis,” J. Chem. Educ. 2002, 79, 360–363. 17.7 https://chem.libretexts.org/@go/page/190402 Herrington, B. L. “A Demonstration of the Necessity for Care in Sampling,” J. Chem. Educ. 1937, 14, 544. Kratochvil, B.; Reid, R. S.; Harris, W. E. “Sampling Error in a Particulate Mixture”, J. Chem. Educ. 1980, 57, 518–520. Ross, M. R. “A Classroom Exercise in Sampling Technique,” J. Chem. Educ. 2000, 77, 1015–1016. Settle, F. A.; Pleva, M. “The Weakest Link Exercise,” Anal. Chem. 1999, 71, 538A–540A. Vitt, J. E.; Engstrom, R. C. “Effect of Sample Size on Sampling Error,” J. Chem. Educ. 1999, 76, 99–100. The following experiments describe homemade sampling devices for collecting samples in the field. Delumyea, R. D.; McCleary, D. L. “A Device to Collect Sediment Cores,” J. Chem. Educ. 1993, 70, 172–173. Rockwell, D. M.; Hansen, T. “Sampling and Analyzing Air Pollution,” J. Chem. Educ. 1994, 71, 318–322. Saxena, S., Upadhyay, R.; Upadhyay, P. “A Simple and Low-Cost Air Sampler,” J. Chem. Educ. 1996, 73, 787–788. Shooter, D. “Nitrogen Dioxide and Its Determination in the Atmosphere,” J. Chem. Educ. 1993, 70, A133–A140. The following experiments introduce students to methods for extracting analytes from their matrix. “Extract-Clean™ SPE Sample Preparation Guide Volume 1”, Bulletin No. 83, Alltech Associates, Inc. Deerfield, IL. Freeman, R. G.; McCurdy, D. L. “Using Microwave Sample Decomposition in Undergraduate Analytical Chemistry,” J. Chem. Educ. 1998, 75, 1033–1032. Snow, N. H.; Dunn, M.; Patel, S. “Determination of Crude Fat in Food Products by Supercritical Fluid Extraction and Gravimetric Analysis,” J. Chem. Educ. 1997, 74, 1108–1111. Yang, M. J.; Orton, M. L.; Pawliszyn, J. “Quantitative Determination of Caffeine in Beverages Using a Combined SPMEGC/MS Method,” J. Chem. Educ. 1997, 74, 1130–1132. The following paper provides a general introduction to the terminology used in describing sampling. “Terminology—The key to understanding analytical science. Part 2: Sampling and sample preparation,” AMC Technical Brief No. 19, March 2005 (link). Majors, R. E. “Nomenclature for Sampling in Analytical Chemistry” LC•GC 1992, 10, 500–506. Further information on the statistics of sampling is covered in the following papers and textbooks. “What is uncertainty from sampling, and why is it important?” AMC Technical Brief No. 16A, June 2004 (link). “Analytical and sampling strategy, fitness for purpose, and computer games,” AMC Technical Brief No. 20, August 2005 (link). “Measurement uncertainty arising from sampling: the new Eurachem Guide,” AMC Technical Brief No. 31, July 2008 (link). Sampling for Analytical Purpose, Gy, P. ed., Wiley: NY, 1998. Baiulescu, G. E.; Dumitrescu, P.; Zuaravescu, P. G. Sampling, Ellis Horwood: NY, 1991. Cohen, R. D. “How the Size of a Random Sample Affects How Accurately It Represents a Population,” J. Chem. Educ. 1992, 74, 1130–1132. Efstathiou, C. E. “On the sampling variance of ultra-dilute solutions,” Talanta 2000, 52, 711–715. Gerlach, R. W.; Dobb, D. E.; Raab, G. A.; Nocerino, J. M. J. Chemom. 2002, 16, 321–328. Gy, P. M. Sampling of Particulate Materials: Theory and Practice; Elsevier: Amsterdam, 1979. Gy, P. M. Sampling of Heterogeneous and Dynamic Materials: Theories of Heterogeneity, Sampling and Homogenizing; Elsevier: Amsterdam, 1992. Kratochvil, B.; Taylor, J. K. “Sampling for Chemical Analysis,” Anal. Chem. 1981, 53, 924A–938A. Kratochvil, B.; Goewie, C. E.; Taylor, J. K. “Sampling Theory for Environmental Analysis,” Trends Anal. Chem. 1986, 5, 253– 256. Meyer, V. R. LC•GC 2002, 20, 106–112. Rohlf, F. J.; Akçakaya, H. R.; Ferraro, S. P. “Optimizing Composite Sampling Protocols,” Environ. Sci. Technol. 1996, 30, 2899–2905. Smith, R.; James, G. V. The Sampling of Bulk Materials; Royal Society of Chemistry: London, 1981. The process of collecting a sample presents a variety of difficulties, particularly with respect to the analyte’s integrity. The following papers provide representative examples of sampling problems. Barceló, D.; Hennion, M. C. “Sampling of Polar Pesticides from Water Matrices,” Anal. Chim. Acta 1997, 338, 3–18. Batley, G. E.; Gardner, D. “Sampling and Storage of Natural Waters for Trace Metal Analysis,” Wat. Res. 1977, 11, 745–756. 17.8 https://chem.libretexts.org/@go/page/190402 Benoit, G.; Hunter, K. S.; Rozan, T. F. “Sources of Trace Metal Contamination Artifacts during Collection, Handling, and Analysis of Freshwaters,” Anal. Chem. 1997, 69, 1006–1011 Brittain, H. G. “Particle-Size Distribution II: The Problem of Sampling Powdered Solids,” Pharm. Technol. July 2002, 67–73. Ramsey, M. H. “Measurement Uncertainty Arising from Sampling: Implications for the Objectives of Geoanalysis,” Analyst, 1997, 122, 1255–1260. Seiler, T-B; Schulze, T.; Hollert, H. “The risk of altering soil and sediment samples upon extract preparation for analytical and bio-analytical investigations—a review,” Anal. Bioanal. Chem. 2008, 390, 1975–1985. The following texts and articles provide additional information on methods for separating analytes and interferents. “Guide to Solid Phase Extraction,” Bulletin 910, Sigma-Aldrich, 1998. “Solid Phase Microextraction: Theory and Optimization of Conditions,” Bulletin 923, Sigma-Aldrich, 1998. Microwave-Enhanced Chemistry: Fundamentals, Sample Preparation, and Applications, Kingston, H. M.; Haswell, S. J., eds.; American Chemical Society: Washington, D.C., 1997. Anderson, R. Sample Pretreatment and Separation, Wiley: Chichester, 1987. Bettiol, C.; Stievano, L.; Bertelle, M.; Delfino, F.; Argese, E. “Evaluation of microwave-assisted acid extraction procedures for the determination of metal content and potential bioavailability in sediments,” Appl. Geochem. 2008, 23, 1140–1151. Compton, T. R. Direct Preconcentration Techniques, Oxford Science Publications: Oxford, 1993. Compton, T. R. Complex-Formation Preconcentration Techniques, Oxford Science Publications: Oxford, 1993. Hinshaw, J. V. “Solid-Phase Microextraction,” LC•GC Europse 2003, December, 2–5. Karger, B. L.; Snyder, L. R.; Harvath, C. An Introduction to Separation Science, Wiley-Interscience: N. Y.; 1973. Majors, R. E.; Raynie, D. E. “Sample Preparation and Solid-Phase Extraction”, LC•GC 1997, 15, 1106–1117. Luque de Castro, M. D.; Priego-Capote, F.; Sánchez-Ávila, N. “Is dialysis alive as a membrane-based separation technique?” Trends Anal. Chem. 2008, 27, 315–326. Mary, P.; Studer, V.; Tabeling, P. “Microfluidic Droplet-Based Liquid–Liquid Extraction,” Anal. Chem. 2008, 80, 2680–2687. Miller, J. M. Separation Methods in Chemical Analysis, Wiley-Interscience: N. Y.; 1975. Morrison, G. H.; Freiser, H. Solvent Extraction in Analytical Chemistry, John Wiley and Sons: N. Y.; 1957. Pawliszyn, J. Solid-Phase Microextraction: Theory and Practice, Wiley: NY, 1997. Pawliszyn, J. “Sample Preparation: Quo Vadis?” Anal. Chem. 2003, 75, 2543–2558. Sulcek, Z.; Povondra, P. Methods of Decomposition in Inorganic Analysis; CRC Press: Boca Raton, FL, 1989. Theis, A. L.; Waldack, A. J.; Hansen, S. M.; Jeannot, M. A. “Headspace Solvent Microextraction,” Anal. Chem. 2001, 73, 5651–5654. Thurman, E. M.; Mills, M. S. Solid-Phase Extraction: Principles and Practice, Wiley: NY, 1998. Zhang, Z.; Yang, M.; Pawliszyn, J. “Solid-Phase Microextraction,” Anal. Chem. 1994, 66, 844A–853A. Chapter 8 The following set of experiments introduce students to the applications of gravimetry. Burrows, H. D.; Ellis, H. A.; Odilora, C. A. “The Dehydrochlorination of PVC,” J. Chem. Educ. 1995, 72, 448–450. Carmosini, N.; Ghoreshy, S. Koether, M. C. “The Gravimetric Analysis of Nickel Using a Microwave Oven,” J. Chem. Educ. 1997, 74, 986–987. Harris, T. M. “Revitalizing the Gravimetric Determination in Quantitative Analysis Laboratory,” J. Chem. Educ. 1995, 72, 355– 356. Henrickson, C. H.; Robinson, P. R. “Gravimetric Determination of Calcium as CaC2O4•H2O,” J. Chem. Educ. 1979, 56, 341– 342. Shaver, L. A. “Determination of Phosphates by the Gravimetric Quimociac Technique,” J. Chem. Educ. 2008, 85, 1097–1098. Snow, N. H.; Dunn, M.; Patel, S. “Determination of Crude Fat in Food Products by Supercritical Fluid Extraction and Gravimetric Analysis,” J. Chem. Educ. 1997, 74, 1108–1111. Thompson, R. Q.; Ghadiali, M. “Microwave Drying of Precipitates for Gravimetric Analysis,” J. Chem. Educ. 1993, 70, 170– 171. Wynne, A. M. “The Thermal Decomposition of Urea,” J. Chem. Educ. 1987, 64, 180–182. The following resources provide a general history of gravimetry. 17.9 https://chem.libretexts.org/@go/page/190402 A History of Analytical Chemistry; Laitinen, H. A.; Ewing, G. W., Eds.; The Division of Analytical Chemistry of the American Chemical Society: Washington, D. C., 1977, pp. 10-24. Beck, C. M. “Classical Analysis: A Look at the Past, Present, and Future,” Anal. Chem. 1991, 63, 993A–1003A; Anal. Chem. 1994, 66, 224A–239A Consult the following texts for additional examples of inorganic and organic gravimetric methods include the following texts. Bassett, J.; Denney, R. C.; Jeffery, G. H.; Mendham, J. Vogel’s Textbook of Quantitative Inorganic Analysis, Longman: London, 4th Ed., 1981. Erdey, L. Gravimetric Analysis, Pergamon: Oxford, 1965. Steymark, A. Quantitative Organic Microanalysis, The Blakiston Co.: NY, 1951. Wendlandt, W. W. Thermal Methods of Analysis, 2nd Ed. Wiley: NY. 1986. For a review of isotope dilution mass spectrometry see the following article. Fassett, J. D.; Paulsen, P. J. “Isotope Dilution Mass Spectrometry for Accurate Elemental Analysis,” Anal. Chem. 1989, 61, 643A–649A. Chapter 9 The following set of experiments introduce students to the applications of titrimetry. Experiments are grouped into four categories based on the type of reaction (acid–base, complexation, redox, and precipitation). Additional experiments emphasizing potentiometric electrodes are found in Chapter 11. Acid–base titrimetry Boiani, J. A. “The Gran Plot Analysis of an Acid Mixture,” J. Chem. Educ. 1986, 63, 724–726. Castillo, C. A.; Jaramillo, A. “An Alternative Procedure for Titration Curves of a Mixture of Acids of Different Strengths,” J. Chem. Educ. 1989, 66, 341. Clark, R. W.; White, G. D.; Bonicamp, J. M.; Watts, E. D. “From Titration Data to Buffer Capacities: A Compter Experiment for the Chemistry Lab or Lecture,” J. Chem. Educ. 1995, 72, 746–750. Clay, J. T.; Walters, E. A.; Brabson, G. D. “A Dibasic Acid Titration for the Physical Chemistry Laboratory” J. Chem. Educ. 1995, 72, 665–667. Crossno, S. K; Kalbus, L. H.; Kalbus, G. E. “Determinations of Carbon Dioxide by Titration,” J. Chem. Educ. 1996, 73, 175– 176. Flowers, P. A. “Potentiometric Measurement of Transition Ranges and Titration Errors for Acid/Base Indicators,” J. Chem. Educ. 1997, 74, 846–847. Fuchsam, W. H.; Garg, Sandhya “Acid Content of Beverages,” J. Chem. Educ. 1990, 67, 67–68 Graham. R.C.; DePew, S. “Determination of Ammonia in Household Cleaners,” J. Chem. Educ. 1983, 60, 765–766. Kalbus, L. H.; Petrucci, R. H.; Forman, J. E.; Kalbus, G. E. “Titration of Chromate-Dichromate Mixtures,” J. Chem. Educ. 1991, 68, 677–678. Kooser, A. S.; Jenkins, J. L.; Welch, L. E. “Acid–Base Indicators: A New Look at an Old Topic,” J. Chem. Educ. 2001, 78, 1504–1506. Kraft, A. “The Determination of the pKa of Multiprotic, Weak Acids by Analyzing Potentiometric Acid–Base Titration Data with Difference Plots,” J. Chem. Educ. 2003, 80, 554–559. Murphy, J. “Determination of Phosphoric Acid in Cola Beverages,” J. Chem. Educ. 1983, 60, 420–421. Nyasulu, F.; Barlag, R.; Macklin, J. Chem. Educator 2008, 13, 289–294. Ophardt, C. E. “Acid Rain Analysis by Standard Addition Titration,” J. Chem. Educ. 1985, 62, 257–258. Partanen, J. I.; Kärki, M. H. “Determination of the Thermodynamic Dissociation Constant of a Weak Acid by Potentiometric Acid-Base Titration,” J. Chem. Educ. 1994, 71, A120–A122. Thompson, R. Q. “Identification of Weak Acids and Bases by Titration with Primary Standards,” J. Chem. Educ. 1988, 65, 179–180. Tucker, S. A.; Amszi, V. L.; Acree, Jr. W. E. “Studying Acid-Base Equilibria in Two-Phase Solvent Media,” J. Chem. Educ. 1993, 70, 80–82. Tucker, S. A.; Acree, Jr., W. E. “A Student-Designed Analytical Laboratory Method,” J. Chem. Educ. 1994, 71, 71–74. Werner, J. A.; Werner, T. C. “Multifunctional Base Unknowns in the Introductory Analytical Chemistry Lab,” J. Chem. Educ. 1991, 68, 600–601. 17.10 https://chem.libretexts.org/@go/page/190402 Complexation Titrimetry Ceretti, H.; Hughes, E. A.; Zalts, A. “The Softening of Hard Water and Complexometric Titrations,” J. Chem. Educ. 1999, 76, 1420–1421. Fulton, R.; Ross, M.; Schroeder, K. “Spectrophotometric Titration of a Mixture of Calcium and Magnesium,” J. Chem. Educ. 1986, 63, 721–723. Novick, S. G. “Complexometric Titration of Zinc,” J. Chem. Educ. 1997, 74, 1463. Olsen, K. G.; Ulicny, L. J. “Reduction of Calcium Concentrations by the Brita Water Filtration System: A Practical Experiment in Titrimetry and Atomic Absorption Spectroscopy,” J. Chem. Educ. 2001, 78, 941. Smith, R. L.; Popham, R. E. “The Quantitative Resolution of a Mixture of Group II Metal Ions by Thermometric Titration with EDTA,” J. Chem. Educ. 1983, 60, 1076–1077. Yappert, M. C.; DuPré, D. B. “Complexometric Titrations: Competition of Complexing Agents in the Determination of Water Hardness with EDTA,” J. Chem. Educ. 1997, 74, 1422–1423. Redox Titrimetry Guenther, W. B. “Supertitrations: High-Precision Methods,” J. Chem. Educ. 1988, 65, 1097–1098. Haddad, P. “Vitamin C Content of Commercial Orange Juices,” J. Chem. Educ. 1977, 54, 192–193. Harris, D. C.; Hills, M. E.; Hewston, T. A. “Preparation, Iodometric Analysis and Classroom Demonstration of Superconductivity in YBa2Cu3O8–x,” J. Chem. Educ. 1987, 64, 847–850. Lau, O.-W.; Luk, S.-F.; Cheng, N. L. N.; Woo, H.-O. “Determination of Free Lime in Clinker and Cement by Iodometry,” J. Chem. Educ. 2001, 78, 1671–1673. Phinyocheep, P.; Tang, I. M. “Determination of the Hole Concentration (Copper Valency) in the High Tc Superconductors,” J. Chem. Educ. 1994, 71, A115–A118. Powell, J. R.; Tucker, S. A.; Acree, Jr., W. E.; Sees, J. A.; Hall, L. M. “A Student-Designed Potentiometric Titration: Quantitative Determination of Iron(II) by Caro’s Acid Titration,” J. Chem. Educ. 1996, 73, 984–986. Precipitation Titrimetry Ueno, K.; Kina, K. “Colloid Titration - A Rapid Method for the Determination of Charged Colloid,” J. Chem. Educ. 1985, 62, 627–629. For a general history of titrimetry, see the following sources. A History of Analytical Chemistry; Laitinen, H. A.; Ewing, G. W., Eds.; The Division of Analytical Chemistry of the American Chemical Society: Washington, D. C., 1977, pp. 52–93. Kolthoff, I. M. “Analytical Chemistry in the USA in the First Quarter of This Century,” Anal. Chem. 1994, 66, 241A–249A. The use of weight instead of volume as a signal for titrimetry is reviewed in the following paper. Kratochvil, B.; Maitra, C. “Weight Titrations: Past and Present,” Am. Lab. 1983, January, 22–29. A more thorough discussion of non-aqueous titrations, with numerous practical examples, is provided in the following text. Fritz, J. S. Acid-Base Titrations in Nonaqueous Solvents; Allyn and Bacon, Boston; 1973. The sources listed below provides more details on the how potentiometric titration data may be used to calculate equilibrium constants. Babić, S.; Horvat, A. J. M.; Pavlović, D. M.; Kaštelan-Macan, M. “Determination of pKa values of active pharmaceutical ingredients,” Trends Anal. Chem. 2007, 26, 1043–1061. Meloun, M.; Havel, J.; Högfeldt, E. Computation of Solution Equilibria, Ellis Horwood Limited: Chichester, England; 1988. The following provides additional information about Gran plots. Michalowski, T.; Kupiec, K.; Rymanowski, M. Anal. Chim. Acta 2008, 606, 172–183. Schwartz, L. M. “Advances in Acid-Base Gran Plot Methodology,” J. Chem. Educ. 1987, 64, 947–950. Schwartz, L. M. “Uncertainty of a Titration Equivalence Point,” J. Chem. Educ. 1992, 69, 879–883. The following provide additional information about calculating or sketching titration curves. Barnum, D. “Predicting Acid–Base Titration Curves without Calculations,” J. Chem. Educ. 1999, 76, 938–942. de Levie, R. “A simple expression for the redox titration curve,” J. Electroanal. Chem. 1992, 323, 347–355. 17.11 https://chem.libretexts.org/@go/page/190402 King, D. W. “A General Approach for Calculating Speciation and Posing Capacity of Redox Systems with Multiple Oxidation States: Application to Redox Titrations and the Generation of pε–pH,” J. Chem. Educ. 2002, 79, 1135–1140. For a complete discussion of the application of complexation titrimetry see the texts listed below. Pribil, R. Applied Complexometry, Pergamon Press: Oxford, 1982. Ringbom, A. Complexation in Analytical Chemistry, John Wiley and Sons, Inc.: New York, 1963. Schwarzenbach, G. Complexometric Titrations, Methuen & Co. Ltd: London, 1957. A good source for additional examples of the application of all forms of titrimetry is Vogel’s Textbook of Quantitative Inorganic Analysis, Longman: London, 4th Ed., 1981. Chapter 10 The following set of experiments introduce students to the applications of spectroscopy. Experiments are grouped into five categories: UV/Vis spectroscopy, IR spectroscopy, atomic absorption and atomic emission, fluorescence and phosphorescence, and signal averaging. UV/Vis Spectroscopy Abney, J. R.; Scalettar, B. A. “Saving Your Students’ Skin. Undergraduate Experiments That Probe UV Protection by Sunscreens and Sunglasses,” J. Chem. Educ. 1998, 75, 757–760. Ainscough, E. W.; Brodie, A. M. “The Determination of Vanillin in Vanilla Extract,” J. Chem. Educ. 1990, 67, 1070–1071. Allen, H. C.; Brauers, T.; Finlayson-Pitts, B. J. “Illustrating Deviations in the Beer-Lambert Law in an Instrumental Analysis Laboratory: Measuring Atmospheric Pollutants by Differential Optical Absorption Spectrometry,” J. Chem. Educ. 1997, 74, 1459–1462. Blanco, M.; Iturriaga, H.; Maspoch, S.; Tarîn, P. “A Simple Method for Spectrophotometric Determination of Two-Components with Overlapped Spectra,” J. Chem. Educ. 1989, 66, 178–180. Bonicamp, J. M.; Martin, K. L.; McBride, G. R.; Clark, R. W. “Beer’s Law is Not a Straight Line: Amplification of Errors by Transformation,” Chem. Educator 1999, 4, 81–88. Bruneau, E.; Lavabre, D.; Levy, G.; Micheau, J. C. “Quantitative Analysis of Continuous-Variation Plots with a Comparison of Several Methods,” J. Chem. Educ. 1992, 69, 833–837. Cappas, C.; Hoffman, N.; Jones, J.; Young, S. “Determination of Concentrations of Species Whose Absorption Bands Overlap Extensively,” J. Chem. Educ. 1991, 68, 300–303. Crisp, P. T.; Eckert, J. M.; Gibson, N. A. “The Determination of Anionic Surfactants in Natural and Waste Waters,” J. Chem. Educ. 1983, 60, 236–238. Dilbeck, C. W.; Ganske, J. A. “Detection of NOx in Automobile Exhaust: An Applied Experiment in Atmospheric/Environmental Chemistry for the General Chemistry Laboratory,” Chem. Educator 2008, 13, 1–5. Domínguez, A., Fernández, A.; González, N.; Iglesias, E.; Montenegro, L. “Determination of Critical Micelle Concentration of Some Surfactants by Three Techniques,” J. Chem. Educ. 1997, 74, 1227–1231. Gilbert, D. D. “Determining Optimum Spectral Bandwidth,” J. Chem. Educ. 1991, 68, A278–A281. Han, J.; Story, T.; Han, G. “A Spectrophotometric Method for Quantitative Determination of Bromine Using Tris(2carboxyethyl)phophine,” J. Chem. Educ. 1999, 76, 976–977. Higginbotham, C.; Pike, C. F.; Rice, J, K. “Spectroscopy in Sol-Gel Matricies,” J. Chem. Educ. 1998, 75, 461–464. Hill, Z. D.; MacCarthy, P. “Novel Approach to Job’s Method,” J. Chem. Educ. 1986, 63, 162–167. Ibañez, G. A.; Olivieri, A. C.; Escandar, G. M. “Determination of Equilibrium Constants of Metal Complexes from Spectrophotometric Measurements,” J. Chem. Educ. 1999, 76, 1277–1281. Long, J. R.; Drago, R. S. “The Rigorous Evaluation of Spectrophotometric Data to Obtain an Equilibrium Constant,” J. Chem. Educ. 1982, 59, 1037–1039. Lozano-Calero; D.; Martin-Palomeque, P. “Determination of Phosphorous in Cola Drinks,” J. Chem. Educ. 1996, 73, 1173– 1174. Maloney, K. M.; Quiazon, E. M.; Indralingam, R. “Measurement of Iron in Egg Yolk: An Instrumental Analysis Measurement Using Biochemical Principles,” J. Chem. Educ. 2008, 85, 399–400. Mascotti, D. P.; Waner, M. J. “Complementary Spectroscopic Assays for Investigation Protein-Ligand Binding Activity: A Project for the Advanced Chemistry Laboratory,” J. Chem. Educ. 2010, 87, 735–738. 17.12 https://chem.libretexts.org/@go/page/190402 McDevitt, V. L.; Rodriquez, A.; Williams, K. R. “Analysis of Soft Drinks: UV Spectrophotometry, Liquid Chromatography, and Capillary Electrophoresis,” J. Chem. Educ. 1998, 75, 625–629. Mehra, M. C.; Rioux, J. “An Analytical Chemistry Experiment in Simultaneous Spectrophotometric Determination of Fe(III) and Cu(II) with Hexacyanoruthenate(II) Reagent,” J. Chem. Educ. 1982, 59, 688–689. Mitchell-Koch, J. T.; Reid, K. R.; Meyerhoff, M. E. “Salicylate Detection by Complexation with Iron(III) and Optical Absorbance Spectroscopy,” J. Chem. Educ. 2008, 85, 1658–1659. Msimanga, H. Z.; Wiese, J. “Determination of Acetaminophen in Analgesics by the Standard Addition Method: A Quantitative Analytical Chemistry Laboratory,” Chem. Educator 2005, 10, 1–7. Örstan, A.; Wojcik, J. F. “Spectroscopic Determination of Protein-Ligand Binding Constants,” J. Chem. Educ. 1987, 64, 814– 816. Pandey, S.; Powell, J. R.; McHale, M. E. R.; Acree Jr., W. E. “Quantitative Determination of Cr(III) and Co(II) Using a Spectroscopic H-Point Standard Addition,” J. Chem. Educ. 1997, 74, 848–850. Parody-Morreale, A.; Cámara-Artigas, A.; Sánchez-Ruiz, J. M. “Spectrophotometric Determination of the Binding Constants of Succinate and Chloride to Glutamic Oxalacetic Transaminase,” J. Chem. Educ. 1990, 67, 988–990. Ravelo-Perez, L. M.; Hernández-Borges, J.; Rodríguez-Delgado, M. A.; Borges-Miquel, T. “Spectrophotometric Analysis of Lycopene in Tomatoes and Watermelons: A Practical Class,” Chem. Educator 2008, 13, 1–3. Russell, D. D.; Potts, J.; Russell, R. M.; Olson, C.; Schimpf, M. “Spectroscopic and Potentiometric Investigation of a Diprotic Acid: An Experimental Approach to Understanding Alpha Functions,” Chem. Educator 1999, 4, 68–72. Smith, E. T.; Matachek, J. R. “A Colorful Investigation of a Diprotic Acid: A General Chemistry Laboratory Exercise,” Chem. Educator 2002, 7, 359–363 Tello-Solis, S. R. “Thermal Unfolding of Lysozyme Studied by UV Difference Spectroscopy,” Chem. Educator 2008, 13, 16– 18. Tucker, S.; Robinson, R.; Keane, C.; Boff, M.; Zenko, M.; Batish, S.; Street, Jr., K. W. “Colorimetric Determination of pH,” J. Chem. Educ. 1989, 66, 769–771. Vitt, J. E. “Troubleshooting 101: An Instrumental Analysis Experiment,” J. Chem. Educ. 2008, 85, 1660–1662. Williams, K. R.; Cole, S. R.; Boyette, S. E.; Schulman, S. G. “The Use of Dristan Nasal Spray as the Unknown for Simultaneous Spectrophotometric Analysis of a Mixture,” J. Chem. Educ. 1990, 67, 535. Walmsley, F. “Aggregation in Dyes: A Spectrophotometric Study,” J. Chem. Educ. 1992, 69, 583. Wells, T. A. “Construction of a Simple Myoglobin-Based Optical Biosensor,” Chem. Educator 2007, 12, 1–3. Yarnelle, M. K.; West, K. J. “Modification of an Ultraviolet Spectrophotometric Determination of the • Active Ingredients in APC Tablets,” J. Chem. Educ. 1989, 66, 601–602. IR Spectroscopy Dragon, S.; Fitch, A. “Infrared Spectroscopy Determination of Lead Binding to Ethylenediaminetetraacetic Acid,” J. Chem. Educ. 1998, 75, 1018–1021. Frohlich, H. “Using Infrared Spectroscopy Measurements to Study Intermolecular Hydrogen Bonding,” J. Chem. Educ. 1993, 70, A3–A6. Garizi, N.; Macias, A.; Furch, T.; Fan, R.; Wagenknecht, P.; Singmaster, K. A. “Cigarette Smoke Analysis Using an Inexpensive Gas-Phase IR Cell,” J. Chem. Educ. 2001, 78, 1665–1666. Indralingam, R.; Nepomuceno, A. I. “The Use of Disposable IR Cards for Quantitative Analysis Using an Internal Standard,” J. Chem. Educ. 2001, 78, 958–960. Mathias, L. J.; Hankins, M. G.; Bertolucci, C. M.; Grubb, T. L.; Muthiah, J. “Quantitative Analysis by FTIR: Thin Films of Copolymers of Ethylene and Vinyl Acetate,” J. Chem. Educ. 1992, 69, A217–A219. Schuttlefield, J. D.; Grassian, V. H. “ATR-FTIR Spectroscopy in the Undergraduate Chemistry Laboratory. Part I: Fundamentals and Examples,” J. Chem. Educ. 2008, 85, 279–281. Schuttlefield, J. D.; Larsen, S. C.; Grassian, V. H. “ATR-FTIR Spectroscopy in the Undergraduate Chemistry Laboratory. Part II: A Physical Chemistry Laboratory Experiment on Surface Adsorption,” J. Chem. Educ. 2008, 85, 282–284. Seasholtz, M. B.; Pence, L. E.; Moe Jr., O. A. “Determination of Carbon Monoxide in Automobile Exhaust by FTIR Spectroscopy,” J. Chem. Educ. 1988, 65, 820–823. Atomic Absorption and Atomic Emission Spectroscopy Amarasiriwardena, D. “Teaching analytical atomic spectroscopy advances in an environmental chemistry class using a projectbased laboratory approach: investigation of lead and arsenic distributions in a lead arsenate contaminated apple orchard,” Anal. 17.13 https://chem.libretexts.org/@go/page/190402 Bioanal. Chem. 2007, 388, 307–314. Buffen, B. P. “Removal of Heavy Metals from Water: An Environmentally Significant Atomic Absorption Spectrometry Experiment,” J. Chem. Educ. 1999, 76, 1678–1679. Dockery, C. R.; Blew, M. J.; Goode, S. R. “Visualizing the Solute Vaporization Interference in Flame Atomic Absorption Spectroscopy,” J. Chem. Educ. 2008, 85, 854–858. Donas, M. K.; Whissel, G.; Dumas, A.; Golden, K. “Analyzing Lead Content in Ancient Bronze Coins by Flame Atomic Absorption Spectroscopy,” J. Chem. Educ. 2009, 86, 343–346. Gilles de Pelichy, L. D.; Adams, C.; Smith, E. T. “Analysis of the Essential Nutrient Strontium in Marine Aquariums by Atomic Absorption Spectroscopy,” J. Chem. Educ. 1997, 74, 1192–1194. Hoskins, L. C.; Reichardt, P. B.; Stolzberg, R. J. “Determination of the Extraction Constant for Zinc Pyrrolidinecarbodithioate,” J. Chem. Educ. 1981, 58, 580–581. Kooser, A. S.; Jenkins, J. L.; Welch, L. E. “Inductively Coupled Plasma-Atomic Emission Spectroscopy: Two Laboratory Activities for the Undergraduate Instrumental Analysis Course,” J. Chem. Educ. 2003, 80, 86–88. Kostecka, K. S. “Atomic Absorption Spectroscopy of Calcium in Foodstuffs in Non-Science-Major Courses,” J. Chem. Educ. 2000, 77, 1321–1323. Lehman, T. A.; Everett, W. W. “Solubility of Lead Sulfate in Water and in Sodium Sulfate Solutions,” J. Chem. Educ. 1982, 59, 797. Markow, P. G. “Determining the Lead Content of Paint Chips,” J. Chem. Educ. 1996, 73, 178–179. Masina, M. R.; Nkosi, P. A.; Rasmussen, P. W.; Shelembe, J. S.; Tyobeka, T. E. “Determination of Metal Ions in Pineapple Juice and Effluent of a Fruit Canning Industry,” J. Chem. Educ. 1989, 66, 342–343. Quigley, M. N. “Determination of Calcium in Analgesic Tablets using Atomic Absorption Spectrophotometry,” J. Chem. Educ. 1994, 71, 800. Quigley, M. N.; Vernon, F. “Determination of Trace Metal Ion Concentrations in Seawater,” J. Chem. Educ. 1996, 73, 671–675. Quigley, M. N.; Vernon, F. “A Matrix Modification Experiment for Use in Electrothermal Atomic Absorption Spectrophotometry,” J. Chem. Educ. 1996, 73, 980–981. Rheingold, A. L.; Hues, S.; Cohen, M. N. “Strontium and Zinc Content in Bones as an Indication of Diet,” J. Chem. Educ. 1983, 60, 233–234. Rocha, F. R. P.; Nóbrega, J. A. “Effects of Solution Physical Properties on Copper and Chromium Signals in Flame Atomic Absorption Spectrometry,” J. Chem. Educ. 1996, 73, 982–984. Fluorescence and Phosphorescence Spectroscopy Buccigross, J. M.; Bedell, C. M.; Suding-Moster, H. L. “Fluorescent Measurement of TNS Binding to Calmodulin,” J. Chem. Educ. 1996, 73, 275–278. Henderleiter, J. A.; Hyslopo, R. M. “The Analysis of Riboflavin in Urine by Fluorescence,” J. Chem. Educ. 1996, 73, 563–564. Lagoria, M. G.; Román, E. S. “How Does Light Scattering Affect Luminescence? Fluorescence Spectra and Quantum Yields in the Solid Form,” J. Chem. Educ. 2002, 79, 1362–1367. Richardson, D. P.; Chang, R. “Lecture Demonstrations of Fluorescence and Phosphorescence,” Chem. Educator 2007, 12, 272– 274. Seixas de Melo, J. S.; Cabral, C.; Burrows, H. D. “Photochemistry and Photophysics in the Laboratory. Showing the Role of Radiationless and Radiative Decay of Excited States,” Chem. Educator 2007, 12, 1–6. Sheffield, M. C.; Nahir, T. M. “Analysis of Selenium in Brazil Nuts by Microwave Digestion and Fluorescence Detection,” J. Chem. Educ. 2002, 79, 1345–1347. Signal Averaging Blitz, J. P.; Klarup, D. G. “Signal-to-Noise Ratio, Signal Processing, and Spectral Information in the Instrumental Analysis Laboratory,” J. Chem. Educ. 2002, 79, 1358–1360. Stolzberg, R. J. “Introduction to Signals and Noise in an Instrumental Method Course,” J. Chem. Educ. 1983, 60, 171–172. Tardy, D. C. “Signal Averaging. A Signal-to-Noise Enhancement Experiment for the Advanced Chemistry Laboratory,” J. Chem. Educ. 1986, 63, 648–650. The following sources provide additional information on spectroscopy in the following areas: general spectroscopy, Beer’s law, instrumentation, Fourier transforms, , IR spectroscopy, atomic absorption and emission, luminescence, and applications. General Spectroscopy 17.14 https://chem.libretexts.org/@go/page/190402 Ball, D. W. “Units! Units! Units!” Spectroscopy 1995, 10(8), 44–47. A History of Analytical Chemistry, Laitinen, H. A.; Ewing, G. W, Eds. The Division of Analytical Chemistry of the American Chemical Society: Washington, D. C., 1977, p103–243. Ingle, J. D.; Crouch, S. R. Spectrochemical Analysis, Prentice Hall, Englewood Cliffs, N. J.; 1988. Macomber, R. S. “A Unifying Approach to Absorption Spectroscopy at the Undergraduate Level,” J. Chem. Educ. 1997, 74, 65–67. Orchin, M.; Jaffe, H. H. Symmetry, Orbitals and Spectra, Wiley-Interscience: New York, 1971. Thomas, N. C. “The Early History of Spectroscopy,” J. Chem. Educ. 1991, 68, 631–633. Beer’s Law Lykos, P. “The Beer-Lambert Law Revisited: A Development without Calculus,” J. Chem. Educ. 1992, 69, 730–732. Ricci, R. W.; Ditzler, M. A.; Nestor, L. P. “Discovering the Beer-Lambert Law,” J. Chem. Educ. 1994, 71, 983–985. Instrumentation Altermose, I. R. “Evolution of Instrumentation for UV-Visible Spectrophotometry: Part I,” J. Chem. Educ. 1986, 63, A216– A223. Altermose, I. R. “Evolution of Instrumentation for UV-Visible Spectrophotometry: Part II,” J. Chem. Educ. 1986, 63, A262– A266. Grossman, W. E. L. “The Optical Characteristics and Production of Diffraction Gratings,” J. Chem. Educ. 1993, 70, 741–748. Jones, D. G. “Photodiode Array Detectors in UV-Vis Spectroscopy: Part I,” Anal. Chem. 1985, 57, 1057A–1073A. Jones, D. G. “Photodiode Array Detectors in UV-Vis Spectroscopy: Part II,” Anal. Chem. 1985, 11, 1207A–1214A. Palmer, C. “Diffraction Gratings,” Spectroscopy, 1995, 10(2), 14–15. Fourier Transforms Bracewell, R. N. “The Fourier Transform,” Sci. American 1989, 260(6), 85–95. Glasser, L. “Fourier Transforms for Chemists: Part I. Introduction to the Fourier Transform,” J. Chem. Educ. 1987, 64, A228– A233. Glasser, L. “Fourier Transforms for Chemists: Part II. Fourier Transforms in Chemistry and Spectroscopy,” J. Chem. Educ. 1987, 64, A260–A266. Glasser, L. “Fourier Transforms for Chemists: Part III. Fourier Transforms in Data Treatment,” J. Chem. Educ. 1987, 64, A306– A313. Graff, D. K. “Fourier and Hadamard: Transforms in Spectroscopy,” J. Chem. Educ. 1995, 72, 304–309. Griffiths, P. R. Chemical Fourier Transform Spectroscopy, Wiley-Interscience: New York, 1975. Transform Techniques in Chemistry, Griffiths, P. R. Ed., Plenum Press: New York, 1978. Perkins, W. E. “Fourier Transform Infrared Spectroscopy: Part I. Instrumentation,” J. Chem. Educ. 1986, 63, A5–A10. Perkins, W. E. “Fourier Transform Infrared Spectroscopy: Part II. Advantages of FT-IR,” J. Chem. Educ. 1987, 64, A269– A271. Perkins, W. E. “Fourier Transform Infrared Spectroscopy: Part III. Applications,” J. Chem. Educ. 1987, 64, A296–A305. Strong III, F. C. “How the Fourier Transform Infrared Spectrophotometer Works,” J. Chem. Educ. 1979, 56, 681–684. IR Spectroscopy Optical Spectroscopy: Sampling Techniques Manual, Harrick Scientific Corporation: Ossining, N. Y., 1987. Leyden, D. E.; Shreedhara Murthy, R. S. “Surface-Selective Sampling Techniques in Fourier Transform Infrared Spectroscopy,” Spectroscopy 1987, 2(2), 28–36. Porro, T. J.; Pattacini, S. C. “Sample Handling for Mid-Infrared Spectroscopy, Part I: Solid and Liquid Sampling,” Spectroscopy 1993, 8(7), 40–47. Porro, T. J.; Pattacini, S. C. “Sample Handling for Mid-Infrared Spectroscopy, Part II: Specialized Techniques,” Spectroscopy 1993, 8(8), 39–44. Atomic Absorption and Emission Blades, M. W.; Weir, D. G. “Fundamental Studies of the Inductively Coupled Plasma,” Spectroscopy 1994, 9, 14–21. Greenfield, S. “Invention of the Annular Inductively Coupled Plasma as a Spectroscopic Source,” J. Chem. Educ. 2000, 77, 584–591. Hieftje, G. M. “Atomic Absorption Spectrometry - Has it Gone or Where is it Going?” J. Anal. At. Spectrom. 1989, 4, 117–122. 17.15 https://chem.libretexts.org/@go/page/190402 Jarrell, R. F. “A Brief History of Atomic Emission Spectrochemical Analysis, 1666-1950,” J. Chem. Educ. 2000, 77, 573–576 Koirtyohann, S. R. “A History of Atomic Absorption Spectrometry From an Academic Perspective,” Anal. Chem. 1991, 63, 1024A–1031A. L’Vov, B. V. “Graphite Furnace Atomic Absorption Spectrometry,” Anal. Chem. 1991, 63, 924A–931A. Slavin, W. “A Comparison of Atomic Spectroscopic Analytical Techniques,” Spectroscopy, 1991, 6, 16–21. Van Loon, J. C. Analytical Atomic Absorption Spectroscopy, Academic Press: New York, 1980. Walsh, A. “The Development of Atomic Absorption Methods of Elemental Analysis 1952-1962,” Anal. Chem. 1991, 63, 933A– 941A. Welz, B. Atomic Absorption Spectroscopy, VCH: Deerfield Beach, FL, 1985. Luminescence Spectroscopy Guilbault, G. G. Practical Fluorescence, Decker: New York, 1990. Schenk, G. “Historical Overview of Fluorescence Analysis to 1980,” Spectroscopy 1997, 12, 47–56. Vo-Dinh, T. Room-Temperature Phosphorimetry for Chemical Analysis, Wiley-Interscience: New York, 1984. Winefordner, J. D.; Schulman, S. G.; O’Haver, T. C. Luminescence Spectroscopy in Analytical Chemistry, Wiley-Interscience: New York, 1969. Applications Trace Analysis and Spectroscopic Methods for Molecules, Christian, G. D.; Callis, J. B. Eds., Wiley-Interscience: New York, 1986. Vandecasteele, C.; Block, C. B. Modern Methods for Trace Element Determination, Wiley: Chichester, England, 1994. Skoog, D. A.; Holler, F. J.; Nieman, T. A. Principles of Instrumental Analysis, Saunders: Philadelphia, 1998. Van Loon, J. C. Selected Methods of Trace Metal Analysis: Biological and Environmental Samples, Wiley-Interscience: New York, 1985. Gathered here are resources and experiments for analyzing multicomponent samples using mathematical techniques not covered in this textbook. Aberasturi, F.; Jimenez, A. I.; Jimenez, F.; Arias, J. J. “UV-Visible First-Derivative Spectrophotometry Applied to an Analysis of a Vitamin Mixture,” J. Chem. Educ. 2001, 78, 793–795. Afkhami, A.; Abbasi-Tarighat, M.; Bahram, M.; Abdollahi, H. “A new strategy for solving matrix effect in multivariate calibration standard addition data using combination of H-point curve isolation and H-point standard addition methods,” Anal. Chim. Acta 2008, 613, 144–151. Brown, C. W.; Obremski, R. J. “Multicomponent Quantitative Analysis,” Appl. Spectrosc. Rev. 1984, 20, 373–418. Charles, M. J.; Martin, N. W.; Msimanga, H. Z. “Simultaneous Determination of Aspirin, Salicylamide, and Caffeine in Pain Relievers by Target Factor Analysis,” J. Chem. Educ. 1997, 74, 1114–1117. Dado, G.; Rosenthal, J. “Simultaneous Determination of Cobalt, Copper, and Nickel by Multivariate Linear Regression,” J. Chem. Educ. 1990, 67, 797–800. DiTusa, M. R.; Schilt, A. A. “Selection of Wavelengths for Optimum Precision in Simultaneous Spectrophotometric Determinations,” J. Chem. Educ. 1985, 62, 541–542. Gómez, D. G.; de la Peña, A. M.; Mansilla, A. E.; Olivieri, A. C. “Spectrophotometric Analysis of Mixtures by Classical LeastSquares Calibration: An Advanced Experiment Introducing MATLAB,” Chem. Educator 2003, 8, 187–191. Harvey, D. T.; Bowman, A. “Factor Analysis of Multicomponent Samples,” J. Chem. Educ. 1990, 67, 470–472. Lucio-Gutierrez, J. R.; Salazar-Cavazos, M. L.; de Torres, N. W. “Chemometrics in the Teaching Lab. Quantification of a Ternary Mixture of Common Pharmaceuticals by First- and Second-Derivative IR Spectroscopy,” Chem. Educator 2004, 9, 234–238. Padney, S.; McHale, M. E. R.; Coym, K. S.; Acree Jr., W. E. “Bilinear Regression Analysis as a Means to Reduce Matrix Effects in Simultaneous Spectrophotometric Determination of Cr(III) and Co(II),” J. Chem. Educ. 1998, 75, 878–880. Raymond, M.; Jochum, C.; Kowalski, B. R. “Optimal Multicomponent Analysis Using the Generalized Standard Addition Method,” J. Chem. Educ. 1983, 60, 1072–1073. Ribone, M. E.; Pagani, A. P.; Olivieri, A. C.; Goicoechea, H. C. “Determination of the Active Principle in a Spectrophotometry and Principal Component Regression Analysis,” J. Chem. Educ. 2000, 77, 1330–1333. Rojas, F. S.; Ojeda, C. B. “Recent developments in derivative ultraviolet/visible absorption spectrophotometry: 2004-2008,” Anal. Chim. Acta 2009, 635, 22–44. 17.16 https://chem.libretexts.org/@go/page/190402 Chapter 11 The following set of experiments introduce students to the applications of electrochemistry. Experiments are grouped into four categories: general electrochemistry, preparation of electrodes, potentiometry, coulometry, and voltammetry and amperometry. General Electrochemistry Mills, K. V.; Herrick, R. S.; Guilmette, L. W.; Nestor, L. P.; Shafer, H.; Ditzler, M. A. “Introducing Undergraduate Students to Electrochemistry: A Two-Week Discovery Chemistry Experiment,” J. Chem. Educ. 2008, 85, 1116–119. Preparation of Electrodes Christopoulos, T. K.; Diamandis, E. P. “Use of a Sintered Glass Crucible for Easy Construction of Liquid-Membrane IonSelective Electrodes,” J. Chem. Educ. 1988, 65, 648. Fricke, G. H.; Kuntz, M. J. “Inexpensive Solid-State Ion-Selective Electrodes for Student Use,” J. Chem. Educ. 1977, 54, 517– 520. Inamdar, S. N.; Bhat, M. A.; Haram, S. K. “Construction of Ag/AgCl Reference Electrode form Used Felt-Tipped Pen Barrel for Undergraduate Laboratory,” J. Chem. Educ. 2009, 86, 355–356. Lloyd, B. W.; O’Brien, F. L.; Wilson, W. D. “Student Preparation and Analysis of Chloride and Calcium Ion Selective Electrodes,” J. Chem. Educ. 1976, 53, 328–330. Mifflin, T. E.; Andriano, K. M.; Robbins, W. B. “Determination of Penicillin Using an Immobilized Enzyme Electrode,” J. Chem. Educ. 1984, 61, 638–639. Palanivel, A.; Riyazuddin, P. “Fabrication of an Inexpensive Ion-Selective Electrode,” J. Chem. Educ. 1984, 61, 290. Ramaley, L; Wedge, P. J.; Crain, S. M. “Inexpensive Instrumental Analysis: Part 1. Ion-Selective Electrodes,” J. Chem. Educ. 1994, 71, 164–167. Selig, W. S. “Potentiometric Titrations Using Pencil and Graphite Sensors,” J. Chem. Educ. 1984, 61, 80–81. Potentiometry Chan, W. H; Wong, M. S.; Yip, C. W. “Ion-Selective Electrode in Organic Analysis: A Salicylate Electrode,” J. Chem. Educ. 1986, 63, 915–916. Harris, T. M. “Potentiometric Measurement in a Freshwater Aquarium,” J. Chem. Educ. 1993, 70, 340–341. Kauffman, C. A.; Muza, A. L.; Porambo, M. W.; Marsh, A. L. “Use of a Commercial Silver-Silver Chloride Electrode for the Measurement of Cell Potentials to Determine Mean Ionic Activity Coefficients,” Chem. Educator 2010, 15, 178–180. Martínez-Fàbregas, E.; Alegret, S. “A Practical Approach to Chemical Sensors through Potentiometric Transducers: Determination of Urea in Serum by Means of a Biosensor,” J. Chem. Educ. 1994, 71, A67–A70. Moresco, H.; Sansón, P.; Seoane, G. “Simple Potentiometric Determination of Reducing Sugars,” J. Chem. Educ. 2008, 85, 1091–1093. Radic, N.; Komijenovic, J. “Potentiometric Determination of an Overall Formation Constant Using an Ion-Selective Membrane Electrode,” J. Chem. Educ. 1993, 70, 509–511. Riyazuddin, P.; Devika, D. “Potentiometric Acid–Base Titrations with Activated Graphite Electrodes,” J. Chem. Educ. 1997, 74, 1198–1199. Coulometry Bertotti, M.; Vaz, J. M.; Telles, R. “Ascorbic Acid Determination in Natural Orange Juice,” J. Chem. Educ. 1995, 72, 445–447. Kalbus, G. E.; Lieu, V. T. “Dietary Fat and Health: An Experiment on the Determination of Iodine Number of Fats and Oils by Coulometric Titration,” J. Chem. Educ. 1991, 68, 64–65. Lötz, A. “A Variety of Electrochemical Methods in a Coulometric Titration Experiment,” J. Chem. Educ. 1998, 75, 775–777. Swim, J.; Earps, E.; Reed, L. M.; Paul, D. “Constant-Current Coulometric Titration of Hydrochloric Acid,” J. Chem. Educ. 1996, 73, 679–683. Voltammetry and Amperometry Blanco-López, M. C.; Lobo-Castañón, M. J.; Miranda-Ordieres, A. J. “Homemade Bienzymatic-Amperometric Biosensor for Beverages Analysis,” J. Chem. Educ. 2007, 84, 677–680. García-Armada, P.; Losada, J.; de Vicente-Pérez, S. “Cation Analysis Scheme by Differential Pulse Polarography,” J. Chem. Educ. 1996, 73, 544–547. 17.17 https://chem.libretexts.org/@go/page/190402 Herrera-Melián, J. A.; Doña-Rodríguez, J. M.; Hernández-Brito, J.; Pérez-Peña, J. “Voltammetric Determination of Ni and Co in Water Samples,” J. Chem. Educ. 1997, 74, 1444–1445. King, D.; Friend, J.; Kariuki, J. “Measuring Vitamin C Content of Commercial Orange Juice Using a Pencil Lead Electrode,” J. Chem. Educ. 2010, 87, 507–509. Marin, D.; Mendicuti, F. “Polarographic Determination of Composition and Thermodynamic Stability Constant of a Complex Metal Ion,” J. Chem. Educ. 1988, 65, 916–918. Sadik, O. A.; Brenda, S.; Joasil, P.; Lord, J. “Electropolymerized Conducting Polymers as Glucose Sensors,” J. Chem. Educ. 1999, 76, 967–970. Sittampalam, G.; Wilson, G. S. “Amperometric Determination of Glucose at Parts Per Million Levels with Immobilized Glucose Oxidase,” J. Chem. Educ. 1982, 59, 70–73. Town, J. L.; MacLaren, F.; Dewald, H. D. “Rotating Disk Voltammetry Experiment,” J. Chem. Educ. 1991, 68, 352–354. Wang, J. “Sensitive Electroanalysis Using Solid Electrodes,” J. Chem. Educ. 1982, 59, 691–692. Wang, J. “Anodic Stripping Voltammetry,” J. Chem. Educ. 1983, 60, 1074–1075. Wang, J.; Maccà, C. “Use of Blood-Glucose Test Strips for Introducing Enzyme Electrodes and Modern Biosensors,” J. Chem. Educ. 1996, 73, 797–800. Wang, Q.; Geiger, A.; Frias, R; Golden, T. D. “An Introduction to Electrochemistry for Undergraduates: Detection of Vitamin C (Ascorbic Acid) by Inexpensive Electrode Sensors,” Chem. Educator 2000, 5, 58–60. The following general references providing a broad introduction to electrochemistry. Adams, R. N. Electrochemistry at Solid Surfaces, Marcel Dekker: New York, 1969. Bard, A. J.; Faulkner, L. R. Electrochemical Methods, Wiley: New York, 1980. Faulkner, L. R. “Electrochemical Characterization of Chemical Systems” in Kuwana, T. E., ed. Physical Methods in Modern Chemical Analysis, Vol. 3, Academic Press: New York, 1983, pp. 137–248. Kissinger, P. T.; Heineman, W. R. Laboratory Techniques in Electroanalytical Chemistry, Marcel Dekker: New York, 1984. Lingane, J. J. Electroanalytical Chemistry, 2nd Ed., Interscience: New York, 1958. Sawyer, D. T.; Roberts, J. L., Jr. Experimental Electrochemistry for Chemists, Wiley-Interscience: New York, 1974. Vassos, B. H.; Ewing, G. W. Electroanalytical Chemistry, Wiley-Interscience: New York, 1983. These short articles provide a good introduction to important principles of electrochemistry. Faulkner, L. R. “Understanding Electrochemistry: Some Distinctive Concepts,” J. Chem. Educ. 1983, 60, 262–264. Huddle, P. A.; White, M. D.; Rogers, F. “Using a Teaching Model to Correct Known Misconceptions in Electrochemistry,” J. Chem. Educ. 2000, 77, 104–110. Maloy, J. T. “Factors Affecting the Shape of Current-Potential Curves,” J. Chem. Educ. 1983, 60, 285–289. Thompson, R. Q.; Craig, N. C. “Unified Electroanalytical Chemistry: Application of the Concept of Equilibrium,” J. Chem. Educ. 2001, 78, 928–934. Zoski, C. G. “Charging Current Discrimination in Analytical Voltammetry,” J. Chem. Educ. 1986, 63, 910–914. Additional information on potentiometry and ion-selective electrodes can be found in the following sources. Bakker, E.; Diamond, D.; Lewenstam, A.; Pretsch, E. “Ions Sensors: Current Limits and New Trends,” Anal. Chim. Acta 1999, 393, 11–18. Bates, R. G. Determination of pH: Theory and Practice, 2nd ed., Wiley: New York, 1973. Buck, R. P. “Potentiometry: pH Measurements and Ion Selective Electrodes” in Weissberger, A., ed. Physical Methods of Organic Chemistry, Vol. 1, Part IIA, Wiley: New York, 1971, pp. 61–162. Cammann, K. Working With Ion-Selective Electrodes, Springer-Verlag: Berlin, 1977. Evans, A. Potentiometry and Ion-Selective Electrodes, Wiley: New York, 1987. Frant, M. S. “Where Did Ion Selective Electrodes Come From?” J. Chem. Educ. 1997, 74, 159–166. Light, T. S. “Industrial Use and Application of Ion-Selective Electrodes,” J. Chem. Educ. 1997, 74, 171–177. Rechnitz, G. A. “Ion and Bio-Selective Membrane Electrodes,” J. Chem. Educ. 1983, 60, 282–284. Ruzicka, J. “The Seventies—Golden Age for Ion-Selective Electrodes,” J. Chem. Educ. 1997, 74, 167–170. Young, C. C. “Evolution of Blood Chemistry Analyzers Based on Ion Selective Electrodes,” J. Chem. Educ. 1997, 74, 177–182. The following sources provide additional information on electrochemical biosensors. Alvarez-Icasa, M.; Bilitewski, U. “Mass Production of Biosensors,” Anal. Chem. 1993, 65, 525A–533A. 17.18 https://chem.libretexts.org/@go/page/190402 Meyerhoff, M. E.; Fu, B.; Bakker, E. Yun, J-H; Yang, V. C. “Polyion-Sensititve Membrane Electrodes for Biomedical Analysis,” Anal. Chem. 1996, 68, 168A–175A. Nicolini, C.; Adami, M; Antolini, F.; Beltram, F.; Sartore, M.; Vakula, S. “Biosensors: A Step to Bioelectronics,” Phys. World, May 1992, 30–34. Rogers, K. R.; Williams. L. R. “Biosensors for Environmental Monitoring: A Regulatory Perspective,” Trends Anal. Chem. 1995, 14, 289–294. Schultz, J. S. “Biosensors,” Sci. Am. August 1991, 64–69. Thompson, M.; Krull, U. “Biosensors and the Transduction of Molecular Recognition,” Anal. Chem. 1991, 63, 393A–405A. Vadgama, P. “Designing Biosensors,” Chem. Brit. 1992, 28, 249–252. A good source covering the clinical application of electrochemistry is listed below. Wang, J. Electroanalytical Techniques in Clinical Chemistry and Laboratory Medicine, VCH: New York, 1998. Coulometry is covered in the following texts. Rechnitz, G. A. Controlled-Potential Analysis, Macmillan: New York, 1963. Milner, G. W. C.; Philips, G. Coulometry in Analytical Chemistry, Pergamon: New York, 1967. For a description of electrogravimetry, see the following resource. Tanaka, N. “Electrodeposition”, in Kolthoff, I. M.; Elving, P. J., eds. Treatise on Analytical Chemistry, Part I: Theory and Practice, Vol. 4, Interscience: New York, 1963. The following sources provide additional information on polarography and pulse polarography. Flato, J. B. “The Renaissance in Polarographic and Voltammetric Analysis,” Anal. Chem. 1972, 44(11), 75A–87A. Kolthoff, I. M.; Lingane, J. J. Polarography, Interscience: New York, 1952. Osteryoung, J. “Pulse Voltammetry,” J. Chem. Educ. 1983, 60, 296–298. Additional Information on stripping voltammetry is available in the following text. Wang, J. Stripping Analysis, VCH Publishers: Deerfield Beach, FL, 1985. The following papers discuss the numerical simulation of voltammetry. Bozzini, B. “A Simple Numerical Procedure for the Simulation of “Lifelike” Linear-Sweep Voltammograms,” J. Chem. Educ. 2000, 77, 100–103. Howard, E.; Cassidy, J. “Analysis with Microelectrodes Using Microsoft Excel Solver,” J. Chem. Educ. 2000, 77, 409–411. Gathered together here are many useful resources for cyclic voltammetry, including experiments. Carriedo, G. A. “The Use of Cyclic Voltammetry in the Study of the Chemistry of Metal–Carbonyls,” J. Chem. Educ. 1988, 65, 1020–1022. García-Jareño, J. J.; Benito, D.; Navarro-Laboulais, J.; Vicente, F. “Electrochemical Behavior of Electrodeposited Prussian Blue Films on ITO Electrodes,” J. Chem. Educ. 1998, 75, 881–884. Gilles de Pelichy, L. D.; Smith, E. T. “A Study of the Oxidation Pathway of Adrenaline by Cyclic Voltammetry,” Chem. Educator 1997, 2(2), 1–13. Gomez, M. E.; Kaifer, A. E. “Voltammetric Behavior of a Ferrocene Derivative,” J. Chem. Educ. 1992, 69, 502–505. Heffner, J. E.; Raber, J. C.; Moe, O. A.; Wigal, C. T. “Using Cyclic Voltammetry and Molecular Modeling to Determine Substituent Effects in the One-Electron Reduction of Benzoquinones,” J. Chem. Educ. 1998, 75, 365–367. Heinze, J. “Cyclic Voltammetry—Electrochemical Spectroscopy,” Angew. Chem, Int. Ed. Eng. 1984, 23, 831–918. Holder, G. N.; Farrar, D. G.; McClure, L. L. “Voltammetric Reductions of Ring-Substituted Acetophenones. 1. Determination of an Electron-Transfer Mechanism Using Cyclic Voltammetry and Computer Modeling: The Formation and Fate of a Radical Anion,” Chem. Educator 2001, 6, 343–349. Ibanez, J. G.; Gonzalez, I.; Cardenas, M. A. “The Effect of Complex Formation Upon the Redox Potentials of Metal Ions: Cyclic Voltammetry Experiments,” J. Chem. Educ. 1988, 65, 173–175. Ito, T.; Perara, D. M. N. T.; Nagasaka, S. “Gold Electrodes Modified with Self-Assembled Monolayers for Measuring LAscobric acid,” J. Chem. Educ. 2008, 85, 1112–1115. Kissinger, P. T.; Heineman, W. R. “Cyclic Voltammetry,” J. Chem. Educ. 1983, 60, 702–706. Mabbott, G. A. “An Introduction to Cyclic Voltammetry,” J. Chem. Educ. 1983, 60, 697–702. 17.19 https://chem.libretexts.org/@go/page/190402 Petrovic, S. “Cyclic Voltammetry of Hexachloroiridate (IV): An Alternative to the Electrochemical Study of the Ferricyanide Ion,” Chem. Educator 2000, 5, 231–235. Toma, H. E.; Araki, K.; Dovidauskas, S. “A Cyclic Voltammetry Experiment Illustrating Redox Potentials, Equilibrium Constants and Substitution Reaction in Coordination Chemistry,” J. Chem. Educ. 2000, 77, 1351–1353. Walczak, M. W.; Dryer, D. A.; Jacobson, D. D,; Foss, M. G.; Flynn, N. T. “pH-Dependent Redox Couple: Illustrating the Nernst Equation Using Cyclic Voltammetry,” J. Chem. Educ. 1997, 74, 1195–1197. Chapter 12 The following set of experiments introduce students to the applications of chromatography and electrophoresis. Experiments are grouped into five categories: gas chromatography, high-performance liquid chromatography, ion-exchange chromatography, sizeexclusion chromatography, and electrophoresis. Gas Chromatography Bishop, R. D., Jr. “Using GC–MS to Determine Relative Reactivity Ratios,” J. Chem. Educ. 1995, 72, 743–745. Elderd, D. M.; Kildahl, N. K.; Berka, L. H. “Experiments for Modern Introductory Chemistry: Identification of Arson Accelerants by Gas Chromatography,” J. Chem. Educ. 1996, 73, 675–677. Fleurat-Lessard, P.; Pointet, K.; Renou-Gonnord, M.-F. “Quantitative Determination of PAHs in Diesel Engine Exhausts by GC–MS,” J. Chem. Educ. 1999, 76, 962–965. Galipo, R. C.; Canhoto, A. J.; Walla, M. D.; Morgan, S. L. “Analysis of Volatile Fragrance and Flavor Compounds by Headspace Solid Phase Microextraction and GC–MS,” J. Chem. Educ. 1999, 76, 245–248. Graham, R. C.; Robertson, J. K. “Analysis of Trihalomethanes in Soft Drinks,” J. Chem. Educ. 1988, 65, 735–737. Heinzen, H.; Moyan, P.; Grompone, A. “Gas Chromatographic Determination of Fatty Acid Compositions,” J. Chem. Educ. 1985, 62, 449–450. Kegley, S. E.; Hansen, K. J.; Cunningham, K. L. “Determination of Polychlorinated Biphenyls (PCBs) in River and Bay Sediments,” J. Chem. Educ. 1996, 73, 558–562. Kostecka, K. S.; Rabah, A.; Palmer, C. F., Jr. “GC/MS Analysis of the Aromatic Composition of Gasoline,” J. Chem. Educ. 1995, 72, 853–854. Quach, D. T.; Ciszkowski, N. A.; Finlayson-Pitts, B. J. “A New GC-MS Experiment for the Undergraduate Instrumental Analysis Laboratory in Environmental Chemistry: Methyl-t-butyl Ether and Benzene in Gasoline,” J. Chem. Educ. 1998, 75, 1595–1598. Ramachandran, B. R.; Allen, J. M.; Halpern, A. M. “Air–Water Partitioning of Environmentally Important Organic Compounds,” J. Chem. Educ. 1996, 73, 1058–1061. Rice, G. W. “Determination of Impurities in Whiskey Using Internal Standard Techniques,” J. Chem. Educ. 1987, 64, 1055– 1056. Rubinson, J. F.; Neyer-Hilvert, J. “Integration of GC-MS Instrumentation into the Undergraduate Laboratory: Separation and Identification of Fatty Acids in Commercial Fats and Oils,” J. Chem. Educ. 1997, 74, 1106–1108. Rudzinski, W. E.; Beu, S. “Gas Chromatographic Determination of Environmentally Significant Pesticides,” J. Chem. Educ. 1982, 59, 614–615. Sobel, R. M.; Ballantine, D. S.; Ryzhov, V. “Quantitation of Phenol Levels in Oil of Wintergreen Using Gas Chromatography– Mass Spectrometry with Selected Ion Monitoring,” J. Chem. Educ. 2005, 82, 601–603. Welch, W. C.; Greco, T. G. “An Experiment in Manual Multiple Headspace Extraction for Gas Chromatography,” J. Chem. Educ. 1993, 70, 333–335. Williams, K. R.; Pierce, R. E. “The Analysis of Orange Oil and the Aqueous Solubility of d-Limone,” J. Chem. Educ. 1998, 75, 223–226. Wong, J. W.; Ngim, K. K.; Shibamoto, T.; Mabury, S. A.; Eiserich, J. P.; Yeo, H. C. H. “Determination of Formaldehyde in Cigarette Smoke,” J. Chem. Educ. 1997, 74, 1100–1103. Yang, M. J.; Orton, M. L., Pawliszyn, J. “Quantitative Determination of Caffeine in Beverages Using a Combined SPMEGC/MS Method,” J. Chem. Educ. 1997, 74, 1130–1132. High-Performance Liquid Chromatography Batchelor, J. D.; Jones, B. T. “Determination of the Scoville Heat Value for Hot Sauces and Chilies: An HPLC Experiment,” J. Chem. Educ. 2000, 77, 266–267. Beckers, J. L. “The Determination of Caffeine in Coffee: Sense or Nonsense?” J. Chem. Educ. 2004, 81, 90–93. 17.20 https://chem.libretexts.org/@go/page/190402 Betts, T. A. “Pungency Quantitation of Hot Pepper Sauces Using HPLC,” J. Chem. Educ. 1999, 76, 240–244. Bidlingmeyer, B. A.; Schmitz, S. “The Analysis of Artificial Sweeteners and Additives in Beverages by HPLC,” J. Chem. Educ. 1991, 68, A195–A200. Bohman, O.; Engdahl, K.-A.; Johnsson, H. “High Performance Liquid Chromatography of Vitamin A: A Quantitative Determination,” J. Chem. Educ. 1982, 59, 251–252. Brenneman, C. A.; Ebeler, S. E. “Chromatographic Separations Using Solid-Phase Extraction Cartridges: Separation of Wine Phenolics,” J. Chem. Educ. 1999, 76, 1710–1711. Cantwell, F. F.; Brown, D. W. “Liquid Chromatographic Determination of Nitroanilines,” J. Chem. Educ. 1981, 58, 820–823. DiNunzio, J. E. “Determination of Caffeine in Beverages by High Performance Liquid Chromatography,” J. Chem. Educ. 1985, 62, 446–447. Ferguson, G. K. “Quantitative HPLC Analysis of an Analgesic/Caffeine Formulation: Determination of Caffeine,” J. Chem. Educ. 1998, 75, 467–469. Ferguson, G. K. “Quantitative HPLC Analysis of a Psychotherapeutic Medication: Simultaneous Determination of Amitriptyline Hydrochloride and Perphenazine,” J. Chem. Educ. 1998, 75, 1615–1618. Goodney, D. E. “Analysis of Vitamin C by High-Pressure Liquid Chromatography,” J. Chem. Educ. 1987, 64, 187–188. Guevremont, R.; Quigley, M. N. “Determination of Paralytic Shellfish Poisons Using Liquid Chromatography,” J. Chem. Educ. 1994, 71, 80–81. Haddad, P.; Hutchins, S.; Tuffy, M. “High Performance Liquid Chromatography of Some Analgesic Compounds,” J. Chem. Educ. 1983, 60, 166–168. Huang, J.; Mabury, S. A.; Sagebiel, J. C. “Hot Chili Peppers: Extraction, Cleanup, and Measurement of Capscaicin,” J. Chem. Educ. 2000, 77, 1630–1631. Joeseph, S. M.; Palasota, J. A. “The Combined Effect of pH and Percent Methanol on the HPLC Separation of Benzoic Acid and Phenol,” J. Chem. Educ. 2001, 78, 1381–1383. Lehame, S. “The Separation of Copper, Iron, and Cobalt Tetramethylene Dithiocarbamates by HPLC,” J. Chem. Educ. 1986, 63, 727–728. Luo, P.; Luo, M. Z.; Baldwin, R. P. “Determination of Sugars in Food Products,” J. Chem. Educ. 1993, 70, 679–681. Mueller, B. L.; Potts, L. W. “HPLC Analysis of an Asthma Medication,” J. Chem. Educ. 1988, 65, 905–906. Munari, M.; Miurin, M.; Goi, G. “Didactic Application to Riboflavin HPLC Analysis,” J. Chem. Educ. 1991, 68, 78–79. Orth, D. L. “HPLC Determination of Taurine in Sports Drinks,” J. Chem. Educ. 2001, 78, 791–792. Remcho, V. T.; McNair, H. M.; Rasmussen, H. T. “HPLC Method Development with the Photodiode Array Detector,” J. Chem. Educ. 1992, 69, A117–A119. Richardson, W. W., III; Burns, L. “HPLC of the Polypeptides in a Hydrolyzate of Egg-White Lysozyme,” J. Chem. Educ. 1988, 65, 162–163. Silveira, A., Jr.; Koehler, J. A.; Beadel, E. F., Jr.; Monore, P. A. “HPLC Analysis of Chlorophyll a, Chlorophyll b, and βCarotene in Collard Greens,” J. Chem. Educ. 1984, 61, 264–265. Siturmorang, M.; Lee, M. T. B.; Witzeman, L. K.; Heineman, W. R. “Liquid Chromatography with Electrochemical Detection (LC-EC): An Experiment Using 4-Aminophenol,” J. Chem. Educ. 1998, 75, 1035–1038. Sottofattori, E.; Raggio, R.; Bruno, O. “Milk as a Drug Analysis Medium: HPLC Determination of Isoniazid,” J. Chem. Educ. 2003, 80, 547–549. Strohl, A. N. “A Study of Colas: An HPLC Experiment,” J. Chem. Educ. 1985, 62, 447–448. Tran, C. D.; Dotlich, M. “Enantiomeric Separation of Beta-Blockers by High Performance Liquid Chromatography,” J. Chem. Educ. 1995, 72, 71–73. Van Arman, S. A.; Thomsen, M. W. “HPLC for Undergraduate Introductory Laboratories,” J. Chem. Educ. 1997, 74, 49–50. Wingen, L. M.; Low, J. C.; Finlayson-Pitts, B. J. “Chromatography, Absorption, and Fluorescence: A New Instrumental Analysis Experiment on the Measurement of Polycyclic Aromatic Hydrocarbons in Cigarette Smoke,” J. Chem. Educ. 1998, 75, 1599–1603. Ion-Exchange Chromatography Bello, M. A.; Gustavo González, A. “Determination of Phosphate in Cola Beverages Using Nonsuppressed Ion Chromatography,” J. Chem. Educ. 1996, 73, 1174–1176. Kieber, R. J.; Jones, S. B. “An Undergraduate Laboratory for the Determination of Sodium, Potassium, and Chloride,” J. Chem. Educ. 1994, 71, A218–A222. Koubek, E.; Stewart, A. E. “The Analysis of Sulfur in Coal,” J. Chem. Educ. 1992, 69, A146–A148. 17.21 https://chem.libretexts.org/@go/page/190402 Sinniah, K.; Piers, K. “Ion Chromatography: Analysis of Ions in Pond Water,” J. Chem. Educ. 2001, 78, 358–362. Xia, K.; Pierzynski, G. “Competitive Sorption between Oxalate and Phosphate in Soil: An Environmental Chemistry Laboratory Using Ion Chromatography,” J. Chem. Educ. 2003, 80, 71–75. Size-Exchange Chromatography Brunauer, L. S.; Davis, K. K. “Size Exclusion Chromatography: An Experiment for High School and Community College Chemistry and Biotechnology Laboratory Programs,” J. Chem. Educ. 2008, 85, 683–685. Saiz, E.; Tarazona, M. P. “Size-Exclusion Chromatography Using Dual Detection,” Chem. Educator 2000, 5, 324–328. Electrophoresis Almarez, R. T.; Kochis, M. “Microscale Capillary Electrophoresis: A Complete Instrumentation Experiment for Chemistry Students at the Undergraduate Junior or Senior Level,” J. Chem. Educ. 2003, 80, 316–319. Beckers, J. L. “The Determination of Caffeine in Coffee: Sense or Nonsense?” J. Chem. Educ. 2004, 81, 90–93. Beckers, J. L. “The Determination of Vanillin in a Vanilla Extract,” J. Chem. Educ. 2005, 82, 604–606. Boyce, M. “Separation and Quantification of Simple Ions by Capillary Zone Electrophoresis,” J. Chem. Educ. 1999, 76, 815– 819. Conradi, S.; Vogt, C.; Rohde, E. “Separation of Enatiomeric Barbiturates by Capillary Electrophoresis Using a CyclodextrinContaining Run Buffer,” J. Chem. Educ. 1997, 74, 1122–1125. Conte, E. D.; Barry, E. F.; Rubinstein, H. “Determination of Caffeine in Beverages by Capillary Zone Electrophoresis,” J. Chem. Educ. 1996, 73, 1169–1170. Demay, S.; Martin-Girardeau, A.; Gonnord, M.-F. “Capillary Electrophoretic Quantitative Analysis of Anions in Drinking Water,” J. Chem. Educ. 1999, 76, 812–815. Emry, R.; Cutright, R. D.; Wright, J.; Markwell, J. “Candies to Dye for: Cooperative, Open-Ended Student Activities to Promote Understanding of Electrophoretic Fractionation,” J. Chem. Educ. 2000, 77, 1323–1324. Gardner, W. P.; Girard, J. E. “Analysis of Common Household Cleaner-Disinfectants by Capillary Electrophoresis,” J. Chem. Educ. 2000, 77, 1335–1338. Gruenhagen, J. A.; Delaware, D.; Ma, Y. “Quantitative Analysis of Non-UV-Absorbing Cations in Soil Samples by HighPerformance Capillary Electrophoresis,” J. Chem. Educ. 2000, 77, 1613–1616. Hage, D. S.; Chattopadhyay, A.; Wolfe, C. A. C.; Grundman, J.; Kelter, P. B. “Determination of Nitrate and Nitrite in Water by Capillary Electrophoresis,” J. Chem. Educ. 1998, 75, 1588–1590. Herman, H. B.; Jezorek, J. R.; Tang, Z. “Analysis of Diet Tonic Water Using Capillary Electrophoresis,” J. Chem. Educ. 2000, 77, 743–744. Janusa, M. A.; Andermann, L. J.; Kliebert, N. M.; Nannie, M. H. “Determination of Chloride Concentration Using Capillary Electrophoresis,” J. Chem. Educ. 1998, 75, 1463–1465. McDevitt, V. L.; Rodríguez, A.; Williams, K. R. “Analysis of Soft Drinks: UV Spectrophotometry, Liquid Chromatography, and Capillary Electrophoresis,” J. Chem. Educ. 1998, 75, 625–629. Palmer, C. P. “Demonstrating Chemical and Analytical Concepts in the Undergraduate Laboratory Using Capillary Electrophoresis and Micellar Electrokinetic Chromatography,” J. Chem. Educ. 1999, 76, 1542–1543. Pursell, C. J.; Chandler, B.; Bushey, M. M. “Capillary Electrophoresis Analysis of Cations in Water Samples,” J. Chem. Educ. 2004, 81, 1783–1786. Solow, M. “Weak Acid pKa Determination Using Capillary Zone Electrophoresis,” J. Chem. Educ. 2006, 83, 1194–1195. Thompson, L.; Veening, H.; Strain, T. G. “Capillary Electrophoresis in the Undergraduate Instrumental Analysis Laboratory: Determination of Common Analgesic Formulations,” J. Chem. Educ. 1997, 74, 1117–1121. Vogt, C.; Conradi, S.; Rhode, E. “Determination of Caffeine and Other Purine Compounds in Food and Pharmaceuticals by Micellar Electrokinetic Chromatography” J. Chem. Educ. 1997, 74, 1126–1130. Weber, P. L.; Buck, D. R. “Capillary Electrophoresis: A Fast and Simple Method for the Determination of the Amino Acid Composition of Proteins,” J. Chem. Educ. 1994, 71, 609–612. Welder, F.; Colyer, C. L. “Using Capillary Electrophoresis to Determine the Purity of Acetylsalicylic Acid Synthesized in the Undergraduate Laboratory,” J. Chem. Educ. 2001, 78, 1525–1527. Williams, K. R.; Adhyaru, B.; German, I.; Russell, T. “Determination of a Diffusion Coefficient by Capillary Electrophoresis,” J. Chem. Educ. 2002, 79, 1475–1476. The following texts provide a good introduction to the broad field of separations, including chromatography and electrophoresis. 17.22 https://chem.libretexts.org/@go/page/190402 Giddings, J. C. Unified Separation Science, Wiley-Interscience: New York 1991. Karger, B. L.; Snyder, L. R.; Harvath, C. An Introduction to Separation Science, Wiley-Interscience: New York, 1973 Miller, J. M. Separation Methods in Chemical Analysis, Wiley-Interscience: New York, 1975. Poole, C. F. The Essence of Chromatography, Elsevier: Amsterdam, 2003. A more recent discussion of peak capacity is presented in the following paper. Davis, J. M.; Stoll, D. R.; Carr, P. W. “Dependence of Effective Peak Capacity in Comprehensive Two-Dimensional Separations on the Distribution of Peak Capacity between the Two Dimensions,” Anal. Chem. 2008, 80, 8122–8134. Li, X.; Stoll, D. R.; Carr, P. W. “Equation for Peak Capacity Estimation in Two-Dimensional Liquid Chromatography,” Anal. Chem. 2009, 81, 845–850. Shen, Y.; Lee, M. “General Equation for Peak Capacity in Column Chromatography,” Anal. Chem. 1998, 70, 3853–3856. The following references may be consulted for more information on gas chromatography. Grob, R. L., ed, Modern Practice of Gas Chromatography, Wiley-Interscience: New York, 1972. Hinshaw, J. V. “A Compendium of GC Terms and Techniques,” LC•GC 1992, 10, 516–522. Ioffe, B. V.; Vitenberg, A. G. Head-Space Analysis and Related Methods in Gas Chromatography, Wiley-Interscience: New York, 1982. Kitson, F. G.; Larsen, B. S.; McEwen, C. N. Gas Chromatography and Mass Spectrometry: A Practical Guide, Academic Press: San Diego, 1996. McMaster, M. C. GC/MS: A Practical User’s Guide, Wiley-Interscience: Hoboken, NJ, 2008. The following references provide more information on high-performance liquid chromatography. Dorschel, C. A.; Ekmanis, J. L.; Oberholtzer, J. E.; Warren, Jr. F. V.; Bidlingmeyer, B. A. “LC Detectors,” Anal. Chem. 1989, 61, 951A–968A. Ehlert, S.; Tallarek, U. “High-pressure liquid chromatography in lab-on-a-chip devices,” Anal. Bioanal. Chem. 2007, 388, 517– 520. Francois, I.; Sandra, K.; Sandra, P. “Comprehensive liquid chromatography: Fundamental aspects and practical considerations —A review,” Anal. Chim. Acta 2009, 641, 14–31. Harris, C. M. “Shrinking the LC Landscape,” Anal. Chem. 2003, 75, 64A–69A. Meyer, V. R. Pitfalls and Errors of HPLC in Pictures, Wiley-VCH: Weinheim, Germany, 2006. Pozo, O. J.; Van Eenoo, P.; Deventer, K.; Delbeke, F. T. “Detection and characterization of anabolic steroids in doping analysis by LC–MS,” Trends Anal. Chem. 2008, 27, 657–671. Scott, R. P. W. “Modern Liquid Chromatography,” Chem. Soc. Rev. 1992, 21, 137–145. Simpson, C. F., ed. Techniques in Liquid Chromatography, Wiley-Hayden: Chichester, England; 1982. Snyder, L. R.; Glajch, J. L.; Kirkland, J. J. Practical HPLC Method Development, Wiley-Interscience: New York,1988. van de Merbel, N. C. “Quantitative determination of endogenous compounds in biological samples using chromatographic techniques,” Trends Anal. Chem. 2008, 27, 924–933. Yeung, E. S. “Chromatographic Detectors: Current Status and Future Prospects,” LC•GC 1989, 7, 118–128. The following references may be consulted for more information on ion chromatography. Shpigun, O. A.; Zolotov, Y. A. Ion Chromatography in Water Analysis, Ellis Horwood: Chichester, England, 1988. Smith, F. C. Jr.; Chang, R. C. The Practice of Ion Chromatography, Wiley-Interscience: New York, 1983. The following references may be consulted for more information on supercritical fluid chromatography. Palmieri, M. D. “An Introduction to Supercritical Fluid Chromatography. Part I: Principles and Applications,” J. Chem. Educ. 1988, 65, A254–A259. Palmieri, M. D. “An Introduction to Supercritical Fluid Chromatography. Part II: Applications and Future Trends,” J. Chem. Educ. 1989, 66, A141–A147. The following references may be consulted for more information on capillary electrophoresis. Baker, D. R. Capillary Electrophoresis, Wiley-Interscience: New York, 1995. Copper, C. L. “Capillary Electrophoresis: Part I. Theoretical and Experimental Background,” J. Chem. Educ. 1998, 75, 343– 347. Copper, C. L.; Whitaker, K. W. “Capillary Electrophoresis: Part II. Applications,” J. Chem. Educ. 1998, 75, 347–351. 17.23 https://chem.libretexts.org/@go/page/190402 DeFrancesco, L. “Capillary Electrophoresis: Finding a Niche,” Today’s Chemist at Work, February 2002, 59–64. Ekins, R. P. “Immunoassay, DNA Analysis, and Other Ligand Binding Assay Techniques: From Electropherograms to Multiplexed, Ultrasensative Microarrays on a Chip,” J. Chem. Educ. 1999, 76, 769–780. Revermann, T.; Götz, S.; Künnemeyer, J.; Karst, U. “Quantitative analysis by microchip capillary electrophoresis—current limitations and problem-solving strategies,” Analyst 2008, 133, 167–174. Timerbaev, A. R. “Capillary electrophoresis coupled to mass spectrometry for biospeciation analysis: critical evaluation,” Trends Anal. Chem. 2009, 28, 416–425. Unger, K. K.; Huber, M.; Hennessy, T. P.; Hearn, M. T. W.; Walhagen, K. “A Critical Appraisal of Capillary Electrochromatography,” Anal. Chem. 2002, 74, 200A–207A. Varenne, A.; Descroix, S. “Recent strategies to improve resolution in capillary electrophoresis—A review,” Anal. Chim. Acta 2008, 628, 9–23. Vetter, A. J.; McGowan, G. J. “The Escalator—An Analogy for Explaining Electroosmotic Flow,” J. Chem. Educ. 2001, 78, 209–211. Xu, Y. “Tutorial: Capillary Electrophoresis,” Chem. Educator, 1996, 1(2), 1–14. The application of spreadsheets and computer programs for modeling chromatography is described in the following papers. Abbay, G. N.; Barry, E. F.; Leepipatpiboon, S.; Ramstad, T.; Roman, M. C.; Siergiej, R. W.; Snyder, L. R.; Winniford, W. L. “Practical Applications of Computer Simulation for Gas Chromatography Method Development,” LC•GC 1991, 9, 100–114. Drouen, A.; Dolan, J. W.; Snyder, L. R.; Poile, A.; Schoenmakers, P. J. “Software for Chromatographic Method Development,” LC•GC 1991, 9, 714–724. Kevra, S. A.; Bergman, D. L.; Maloy, J. T. “A Computational Introduction to Chromatographic Bandshape Analysis,” J. Chem. Educ. 1994, 71, 1023–1028. Rittenhouse, R. C. “HPLC for Windows: A Computer Simulation of High-Performance Liquid Chromatography,” J. Chem. Educ. 1995, 72, 1086–1087. Shalliker, R. A.; Kayillo, S.; Dennis, G. R. “Optimizing Chromatographic Separations: An Experiment Using an HPLC Simulator,” J. Chem. Educ. 2008, 85, 1265–1268. Sundheim, B. R. “Column Operations: A Spreadsheet Model,” J. Chem. Educ. 1992, 69, 1003–1005. The following papers discuss column efficiency, peak shapes, and overlapping chromatographic peaks. Bildingmeyer, B. A.; Warren, F. V., Jr. “Column Efficiency Measurement,” Anal. Chem. 1984, 56, 1583A–1596A. Hawkes, S. J. “Distorted Chromatographic Peaks,” J. Chem. Educ. 1994, 71, 1032–1033. Hinshaw, J. “Pinning Down Tailing Peaks,” LC•GC 1992, 10, 516–522. Meyer, V. K. “Chromatographic Integration Errors: A Closer Look at a Small Peak,” LC•GC North America 2009, 27, 232– 244. Reid, V. R.; Synovec, R. E. “High-speed gas chromatography: The importance of instrumentation optimization and the elimination of extra-column band broadening,” Talanta2008, 76, 703–717. Chapter 13 The following set of experiments introduce students to the applications of chemical kinetic methods, including enzyme kinetic methods, and flow injection analysis. Chemical Kinetic Methods Abramovitch, D. A.; Cunningham, L. K.; Litwer, M. R. “Decomposition Kinetics of Hydrogen Perox- ide: Novel Lab Experiments Employing Computer Technology,” J. Chem. Educ. 2003, 80, 790–792. Bateman, Jr. R. C.; Evans, J. A. “Using the Glucose Oxidase/Peroxidase Systems in Enzyme Kinetics,” J. Chem. Educ. 1995, 72, A240–A241. Bendinskas, K.; DiJacomo, C.; Krill, A.; Vitz, E. “Kinetics of Alcohol Dehydrogenase-Catalyzed Oxidation of Ethanol Followed by Visible Spectroscopy,” J. Chem. Educ. 1068, 82, 1068–1070. Clark, C. R. “A Stopped-Flow Kinetics Experiment for Advanced Undergraduate Laboratories: Formation of Iron(III) Thiocyanate,” J. Chem. Educ. 1997, 74, 1214–1217. Diamandis, E. P.; Koupparis, M. A.; Hadjiionnou, T. P. “Kinetic Studies with Ion-Selective Electrodes: Determination of Creatinine in Urine with a Picrate Ion-Selective Electrode,” J. Chem. Educ. 1983, 60, 74–76. 17.24 https://chem.libretexts.org/@go/page/190402 Frey, M. W.; Frey, S. T.; Soltau, S. R. “Exploring the pH Dependence of L-leucine-p-nitroanilide Cleavage by Aminopeptidase Aeromonas Proteolytica: A Combined Buffer-Enzyme Kinetics Experiment for the General Chemistry Laboratory,” Chem. Educator 2010, 15, 117-120. Gooding, J. J.; Yang, W.; Situmorang, M. “Bioanalytical Experiments for the Undergraduate Laboratory: Monitoring Glucose in Sport Drinks,” J. Chem. Educ. 2001, 78, 788–790. Hamilton, T. M.; Dobie-Galuska, A. A.; Wietstock, S. M. “The o-Phenylenediamine-Horseradish Peroxidase System: Enzyme Kinetics in the General Chemistry Lab,” J. Chem. Educ. 1999, 76, 642– 644. Johnson, K. A. “Factors Affecting Reaction Kinetics of Glucose Oxidase,” J. Chem. Educ. 2002, 79,74–76. Mowry, S.; Ogren, P. J. “Kinetics of Methylene Blue Reduction by Ascorbic Acid,” J. Chem. Educ. 1999, 76, 970–974. Nyasulu, F. W.; Barlag, R. “Gas Pressure Sensor Monitored Iodide-Catalyzed Decomposition Kinetics of Hydrogen Peroxide: An Initial Rate Approach,” Chem. Educator 2008, 13, 227–230. Nyasulu, F. W.; Barlag, R. “Thermokinetics: Iodide-Catalyzed Decomposition Kinetics of Hydrogen Peroxide; An Integrated Rate Approach,” Chem. Educator 2010, 15, 168–170. Pandey, S.; McHale, M. E. R.; Horton, A. M.; Padilla, S. A.; Trufant, A. L.; De La Sancha, N. U.; Vela, E.; Acree, Jr., W. E. “Kinetics-Based Indirect Spectrophotometric Method for the Simultaneous Determination of MnO4–and Cr2O72–,” J. Chem. Educ. 1998, 75, 450–452. Stock, E.; Morgan, M. “A Spectroscopic Analysis of the Kinetics of the Iodine Clock Reaction without Starch,” Chem. Educator 2010, 15, 158–161. Vasilarou, A.-M. G.; Georgiou, C. A. “Enzymatic Spectrophotometric Reaction Rate Determination of Glucose in Fruit Drinks and Carbonated Beverages,” J. Chem. Educ. 2000, 77, 1327–1329. Williams, K. R.; Adhyaru, B.; Timofeev, J.; Blankenship, M. K. “Decomposition of Aspartame. A Kinetics Experiment for Upper-Level Chemistry Laboratories,” J. Chem. Educ. 2005, 82, 924–925. Flow Injection Methods Carroll, M. K.; Tyson, J. F. “An Experiment Using Time-Based Detection in Flow Injection Analysis,” J. Chem. Educ. 1993, 70, A210–A216. Conceição, A. C. L.; Minas da Piedade, M. E. “Determination of Acidity Constants by Gradient Flow-Injection Titration,” J. Chem. Educ. 2006, 83, 1853–1856. Hansen, E. H.; Ruzicka, J. “The Principles of Flow Injection Analysis as Demonstrated by Three Lab Exercises,” J. Chem. Educ. 1979, 56, 677–680. McKelvie, I. D.; Cardwell, T. J.; Cattrall, R. W. “A Microconduit Flow Injection Analysis Demonstration using a 35-mm Slide Projector,” J. Chem. Educ. 1990, 67, 262–263. Meyerhoff, M. E.; Kovach, P. M. “An Ion-Selective Electrode/Flow Injection Analysis Experiment: Determination of Potassium in Serum,” J. Chem. Educ. 1983, 60, 766–768. Nóbrega, J. A.; Rocha, F. R. P. “Ionic Strength Effect on the Rate of Reduction of Hexacyanoferrate(II) by Ascorbic Acid,” J. Chem. Educ. 1997, 74, 560–562. Ríos, A.; Luque de Castro, M.; Valcárcel, M. “Determination of Reaction Stoichiometries by Flow Injection Analysis,” J. Chem. Educ. 1986, 63, 552–553. Stults, C. L. M.; Wade, A. P.; Crouch, S. R. “Investigation of Temperature Effects on Dispersion in a Flow Injection Analyzer,” J. Chem. Educ. 1988, 65, 645–647. Wolfe, C. A. C.; Oates, M. R.; Hage, D. S. “Automated Protein Assay Using Flow Injection Analysis,” J. Chem. Educ. 1998, 75, 1025–1028. The following sources provides a general review of the importance of chemical kinetics in analytical chemistry. Bergmyer, H. U.; Grassl, M. Methods of Enzymatic Analysis, Verlag Chemie: Deerfield Beach, FL, 3rd Ed., 1983. Laitinen, H. A.; Ewing, G. W., eds., A History of Analytical Chemistry, The Division of Analytical Chemistry of the American Chemical Society: Washington, D. C., 1977, pp. 97–102. Malmstadt, H. V.; Delaney, C. J.; Cordos, E. A. “Reaction-Rate Methods of Chemical Analysis,” Crit. Rev. Anal. Chem. 1972, 2, 559–619. Mark, H. B.; Rechnitz, G. A. Kinetics in Analytical Chemistry, Wiley: New York, 1968. 17.25 https://chem.libretexts.org/@go/page/190402 Mottola, H. A. “Catalytic and Differential Reaction-Rate Methods of Chemical Analysis,” Crit. Rev. Anal. Chem. 1974, 4, 229– 280. Mottola, H. A. “Some Kinetic Aspects Relevant to Contemporary Analytical Chemistry,” J. Chem. Educ. 1981, 58, 399–403. Mottola, H. A. Kinetic Aspects of Analytical Chemistry, Wiley: New York, 1988. Pardue, H. L. “A Comprehensive Classification of Kinetic Methods of Analysis Used in Clinical Chemistry,” Clin. Chem. 1977, 23, 2189–2201. Pardue, H. L. “Kinetic Aspects of Analytical Chemistry,” Anal. Chim. Acta, 1989, 216, 69–107. Perez-Bendito, D.; Silva, M. Kinetic Methods in Analytical Chemistry, Ellis Horwood: Chichester, 1988. Pisakiewicz, D. Kinetics of Chemical and Enzyme-Catalyzed Reactions, Oxford University Press: New York, 1977. The following instrumental analysis textbooks may be consulted for further information on the detectors and signal analyzers used in radiochemical methods of analysis. Skoog, D. A.; Holler, F. J.; Nieman, T. A. Principles of Instrumental Analysis, 5th Ed., Saunders College Publishing/Harcourt Brace and Co.: Philadelphia., 1998, Chapter 32. Strobel, H. A.; Heineman, W. R. Chemical Instrumentation: A Systematic Approach, 3rd Ed., Wiley-Interscience: New York, 1989. The following resources provide additional information on the theory and application of flow injection analysis. Andrew, K. N.; Blundell, N. J.; Price, D.; Worsfold, P. J. “Flow Injection Techniques for Water Monitoring,” Anal. Chem. 1994, 66, 916A–922A. Betteridge, D. “Flow Injection Analysis,” Anal. Chem. 1978, 50, 832A–846A. Kowalski, B. R.; Ruzicka, J. Christian, G. D. “Flow Chemography - The Future of Chemical Education,” Trends Anal. Chem. 1990, 9, 8–13. Mottola, H. A. “Continuous Flow Analysis Revisited,” Anal. Chem. 1981, 53, 1312A–1316A. Ruzicka, J. “Flow Injection Analysis: From Test Tube to Integrated Microconduits,” Anal. Chem. 1983, 55, 1040A–1053A. Ruzicka, J.; Hansen, E. H. Flow-Injection Analysis, Wiley-Interscience: New York, 1989. Ruzicka, J.; Hansen, E. H. “Retro-Review of Flow-Injection Analysis,” Trends Anal. Chem. 2008, 27,390–393. Silvestre, C. I. C.; Santos, J. L. M.; Lima, J. L. F. C.; Zagatto, E. A. G. “Liquid-Liquid Extraction in Flow Analysis: A Critical Review,” Anal. Chim. Acta 2009, 652, 54–65. Stewart, K. K. “Flow Injection Analysis: New Tools for Old Assays, New Approaches to Analytical Measurements,” Anal. Chem. 1983, 55, 931A–940A. Tyson, J. F. “Atomic Spectrometry and Flow Injection Analysis: A Synergic Combination,” Anal. Chim. Acta, 1988, 214, 57– 75. Valcarcel, M.; Luque de Castro, M. D. Flow-Injection Analysis: Principles and Applications, Ellis Horwood: Chichester, England, 1987. Chapter 14 The following set of experiments provide practical examples of the optimization of experimental conditions. Examples include simplex optimization, factorial designs for developing empirical models of response surfaces, and fitting experimental data to theoretical models of the response surface. Amenta, D. S.; Lamb, C. E.; Leary, J. J. “Simplex Optimization of Yield of sec-Butylbenzene in a Friedel-Crafts Alkylation,” J. Chem. Educ. 1979, 56, 557–558. Harvey, D. T.; Byerly, S.; Bowman, A.; Tomlin, J. “Optimization of HPLC and GC Separations Using Response Surfaces,” J. Chem. Educ. 1991, 68, 162–168. Leggett, D. L. “Instrumental Simplex Optimization,” J. Chem. Educ. 1983, 60, 707–710. Oles, P. J. “Fractional Factorial Experimental Design as a Teaching Tool for Quantitative Analysis,” J. Chem. Educ. 1998, 75, 357–359. Palasota, J. A.; Deming, S.N. “Central Composite Experimental Design,” J. Chem. Educ. 1992, 69, 560–561. Sangsila, S.; Labinaz, G.; Poland, J. S.; vanLoon, G. W. “An Experiment on Sequential Simplex Optimization of an Atomic Absorption Analysis Procedure,” J. Chem. Educ. 1989, 66, 351–353. 17.26 https://chem.libretexts.org/@go/page/190402 Santos-Delgado, M. J.; Larrea-Tarruella, L. “A Didactic Experience of Statistical Analysis for the Determination of Glycine in a Nonaqueous Medium using ANOVA and a Computer Program,” J. Chem. Educ. 2004, 81, 97–99. Shavers, C. L.; Parsons, M. L.; Deming, S. N. “Simplex Optimization of Chemical Systems,” J. Chem Educ. 1979, 56, 307– 309. Stieg, S. “A Low-Noise Simplex Optimization Experiment,” J. Chem. Educ. 1986, 63, 547–548. Stolzberg, R. J. “Screening and Sequential Experimentation: Simulations and Flame Atomic Absorption Spectrometry Experiments,” J. Chem. Educ. 1997, 74, 216–220. Van Ryswyk, H.; Van Hecke, G. R. “Attaining Optimal Conditions,” J. Chem. Educ. 1991, 66, 878–882. The following texts and articles provide an excellent discussion of optimization methods based on searching algorithms and mathematical modeling use factorial designs, including a discussion of the relevant calculations. A few of these sources discuss other types of experimental designs. Bayne, C. K.; Rubin, I. B. Practical Experimental Designs and Optimization Methods for Chemists, VCH Publishers: Deerfield Beach, FL; 1986. Box, G. E. P. “Statistical Design in the Study of Analytical Methods,” Analyst 1952, 77, 879–891. Deming, S. N.; Morgan, S. L. Experimental Design: A Chemometric Approach, Elsevier: Amsterdam, 1987. Ferreira, S. L. C.; dos Santos, W. N. L.; Quintella, C. M.; Neto, B. B.; Bosque-Sendra, J. M. “Doehlert • Matrix: A Chemometric Tool for Analytical Chemistry—Review,” Talanta 2004, 63, 1061–1067. Ferreira, S. L. C.; Bruns, R. E.; Ferreira, H. S.; Matos, G. D.; David, J. M.; Brandão, G. C.; da Silva, E. G. P.; Portugal, L. A.; dos Reis, P. S.; Souza, A. S.; dos Santos, W. N. L. “Box-Behnken Design: An Alternative for the Optimization of Analytical Methods,” Anal. Chim. Acta 2007, 597, 179–186. Gonzalez, A. G. “Two Level Factorial Experimental Designs Based on Multiple Linear Regression Models: A Tutorial Digest Illustrated by Case Studies,” Anal. Chim. Acta 1998, 360, 227–241. Goupy, J. “What Kind of Experimental Design for Finding and Checking Robustness of Analytical Methods?” Anal. Chim. Acta 2005, 544, 184–190. Hendrix, C. D. “What Every Technologist Should Know About Experimental Design,” Chemtech 1979, 9, 167–174. Hendrix, C. D. “Through the Response Surface with Test Tube and Pipe Wrench,” Chemtech 1980, 10, 488–497. Leardi, R. “Experimental Design: A Tutorial,” Anal. Chim. Acta 2009, 652, 161–172. Liang, Y. “Comparison of Optimization Methods,” Chromatography Review 1985, 12(2), 6–9. Morgan, E. Chemometrics: Experimental Design, John Wiley and Sons: Chichester, 1991. Thompson, M., ed. “Experimental Design and Optimization (1): An Introduction to Some Basic Concepts,” AMC Technical Brief 24, June 2006. Thompson, M., ed. “Experimental Design and Optimization (2): Handling Uncontrolled Factors” AMC Technical Brief 26, December 2006. Thompson, M., ed. “Experimental Design and Optimization (3): Some Fractional Factorial Designs,” AMC Technical Brief 36, January 2009. Walters, F. H.; Morgan, S. L.; Parker, L. P., Jr.; Deming, S. N. Sequential Simplex Optimization, CRC Press: Boca Raton, FL, 1991. (an electronic version of this text is freely available from Multisimplex AB and is available here.) The following texts provide additional information about ANOVA calculations, including discussions of two-way analysis of variance. Graham, R. C. Data Analysis for the Chemical Sciences, VCH Publishers: New York, 1993. Miller, J. C.; Miller, J. N. Statistics for Analytical Chemistry, Ellis Horwood Limited: Chichester, 1988. The following resources provide additional information on the validation of analytical methods. Gonzalez, A. G.; Herrador, M. A. “A Practical Guide to Analytical Method Validation, Including Measurement Uncertainty and Accuracy Profiles,” Trends Anal. Chem. 2007, 26, 227–238. Thompson, M.; Ellison, S. L. R.; Wood, R. “Harmonized Guidelines for Single-Laboratory Validation of Analytical Methods,” Pure Appl. Chem. 2002, 74, 835–855. 17.27 https://chem.libretexts.org/@go/page/190402 Chapter 15 The following three experiments introduce aspects of quality assurance and quality control. Bell, S. C.; Moore, J. “Integration of Quality Assurance/Quality Control into Quantitative Analysis,” J. Chem. Educ. 1998, 75, 874–877. Cancilla, D. A. “Integration of Environmental Analytical Chemistry with Environmental Law: The Development of a ProblemBased Laboratory,” J. Chem. Educ. 2001, 78, 1652–1660. Laquer, F. C. “Quality Control Charts in the Quantitative Analysis Laboratory Using Conductance Measurement,” J. Chem. Educ. 1990, 67, 900–902. Marcos, J.; Ríos, A.; Valcárcel, M. “Practicing Quality Control in a Bioanalytical Experiment,” J. Chem. Educ. 1995, 72, 947– 949. The following texts and articles may be consulted for an additional discussion of quality assurance and quality control. Amore, F. “Good Analytical Practices,” Anal. Chem. 1979, 51, 1105A–1110A. Barnard, Jr. A. J.; Mitchell, R. M.; Wolf, G. E. “Good Analytical Practices in Quality Control,” Anal. Chem. 1978, 50, 1079A– 1086A. Cairns, T.; Rogers, W. M. “Acceptable Analytical Data for Trace Analysis,” Anal. Chem. 1993, 55, 54A–57A. Taylor, J. K. Quality Assurance of Chemical Measurements, Lewis Publishers: Chelsa, MI, 1987. Additional information about the construction and use of control charts may be found in the following sources. Miller, J. C.; Miller, J. N. Statistics for Analytical Chemistry, 2nd Ed., Ellis Horwood Limited: Chichester, 1988. Ouchi, G. I. “Creating Control Charts with a Spreadsheet Program,” LC•GC 1993, 11, 416–423. Ouchi, G. I. “Creating Control Charts with a Spreadsheet Program,” LC•GC 1997, 15, 336–344. Simpson, J. M. “Spreadsheet Statistics,” J. Chem. Educ. 1994, 71, A88–A89. Contributors David Harvey (DePauw University) This page titled 17: Additional Resources is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by David Harvey. 17.28 https://chem.libretexts.org/@go/page/190402 CHAPTER OVERVIEW 18: Back Matter 18.1 https://chem.libretexts.org/@go/page/190403 Front Matter This page was auto-generated because a user created a sub-page to this page. 1 https://chem.libretexts.org/@go/page/191311 Table of Contents Analytical chemistry spans nearly all areas of chemistry but involves the development of tools and methods to measure physical properties of substances and apply those techniques to the identification of their presence (qualitative analysis) and quantify the amount present (quantitative analysis) of species in a wide variety of settings. 1: Front Matter 1.1: TitlePage 1.2: InfoPage 1.3: Table of Contents 2: Introduction to Analytical Chemistry 2.1: What is Analytical Chemistry? 2.2: The Analytical Perspective 2.3: Common Analytical Problems 2.4: Introduction to Analytical Chemistry (Exercises) 2.5: Introduction to Analytical Chemistry (Summary) 3: Basic Tools of Analytical Chemistry In the chapters that follow we will explore many aspects of analytical chemistry. In the process we will consider important questions such as “How do we treat experimental data?”, “How do we ensure that our results are accurate?”, “How do we obtain a representative sample?”, and “How do we select an appropriate analytical technique?” Before we look more closely at these and other questions, we will first review some basic tools of importance to analytical chemists. 3.1: Measurements in Analytical Chemistry 3.2: Concentration 3.3: Stoichiometric Calculations 3.4: Basic Equipment 3.5: Preparing Solutions 3.6: Spreadsheets and Computational Software 3.7: The Laboratory Notebook 3.8: Basic Tools of Analytical Chemistry (Exercises) 3.9: Basic Tools of Analytical Chemistry (Summary) 1 https://chem.libretexts.org/@go/page/191312 4: The Vocabulary of Analytical Chemistry If you leaf through an issue of the journal Analytical Chemistry, you will soon discover that the authors and readers share a common vocabulary of analytical terms. You are probably familiar with some of these terms, such as accuracy and precision, but other terms, such as analyte and matrix may be less familiar to you. In order to participate in the community of analytical chemists, you must first understand its vocabulary. 4.1: Analysis, Determination, and Measurement 4.2: Techniques, Methods, Procedures, and Protocols 4.3: Classifying Analytical Techniques 4.4: Selecting an Analytical Method 4.5: Developing the Procedure 4.6: Protocols 4.7: The Importance of Analytical Methodology 4.8: The Vocabulary of Analytical Chemistry (Exercises) 4.9: The Vocabulary of Analytical Chemistry (Summary) 5: Evaluating Analytical Data When using an analytical method we make three separate evaluations of experimental error. First, before beginning an analysis we evaluate potential sources of errors to ensure that they will not adversely effect our results. Second, during the analysis we monitor our measurements to ensure that errors remain acceptable. Finally, at the end of the analysis we evaluate the quality of the measurements and results, comparing them to our original design criteria. 5.1: Characterizing Measurements and Results 5.2: Characterizing Experimental Errors 5.3: Propagation of Uncertainty 5.4: The Distribution of Measurements and Results 5.5: Statistical Analysis of Data 5.6: Statistical Methods for Normal Distributions 5.7: Detection Limits 5.8: Using Excel and R to Analyze Data 5.9: Evaluating Analytical Data (Exercises) 5.10: Evaluating Analytical Data (Summary) 2 https://chem.libretexts.org/@go/page/191312 6: Standardizing Analytical Methods Standardization is the process of determining the relationship between the signal and the amount of analyte in a sample. Previously, we defined this relationship as Stotal=kACA+Sreag where Stotal is the signal, nA is the moles of analyte, CA is the analyte’s concentration, kA is the method’s sensitivity for the analyte, and Sreag is the contribution to Stotal from sources other than the sample. To standardize a method we must determine values for kA and Sreag, which is the subject of this chapt 6.1: Analytical Standards 6.2: Calibrating the Signal 6.3: Determining the Sensitivity 6.4: Linear Regression and Calibration Curves 6.5: Blank Corrections 6.6: Using Excel and R for a Regression Analysis 6.7: Standardizing Analytical Methods (Exercises) 6.8: Standardizing Analytical Methods (Summary) 7: Equilibrium Chemistry Regardless of the problem on which an analytical chemist is working, its solution requires a knowledge of chemistry and the ability to apply that knowledge. For example, an analytical chemist studying the effect of pollution on spruce trees needs to know the chemical differences between p‑hydroxybenzoic acid and p‑hydroxyacetophenone, two phenols found in the needles of spruce trees. Your ability to “think as a chemist” is a product of your experience in the classroom and in the laboratory. 7.1: Reversible Reactions and Chemical Equilibria 7.2: Thermodynamics and Equilibrium Chemistry 7.3: Manipulating Equilibrium Constants 7.4: Equilibrium Constants for Chemical Reactions 7.5: Le Châtelier’s Principle 7.6: Ladder Diagrams 7.7: Solving Equilibrium Problems 7.8: Buffer Solutions 7.9: Activity Effects 7.10: Using Excel and R to Solve Equilibrium Problems 7.11: Some Final Thoughts on Equilibrium Calculations 7.12: Equilibrium Chemistry (Exercises) 7.13: Equilibrium Chemistry (Summary) 3 https://chem.libretexts.org/@go/page/191312 8: Collecting and Preparing Samples When we use an analytical method to solve a problem, there is no guarantee that our results will be accurate or precise. In designing an analytical method we consider potential sources of determinate error and indeterminate error, and take appropriate steps to minimize their effect, such as including reagent blanks and calibrating instruments. Why might a carefully designed analytical method give poor results? One possibility is that we may have failed to account for errors with the sample. 8.1: The Importance of Sampling 8.2: Designing a Sampling Plan 8.3: Implementing the Sampling Plan 8.4: Separating the Analyte from Interferents 8.5: General Theory of Separation Efficiency 8.6: Classifying Separation Techniques 8.7: Liquid–Liquid Extractions 8.8: Separation Versus Preconcentration 8.9: Collecting and Preparing Samples (Exercises) 8.10: Collecting and Preparing Samples (Summary) 9: Gravimetric Methods Gravimetry includes all analytical methods in which the analytical signal is a measurement of mass or a change in mass. When you step on a scale after exercising you are making, in a sense, a gravimetric determination of your mass. Mass is the most fundamental of all analytical measurements, and gravimetry is unquestionably our oldest quantitative analytical technique. 9.1: Overview of Gravimetric Methods 9.2: Precipitation Gravimetry 9.3: Volatilization Gravimetry 9.4: Particulate Gravimetry 9.5: Gravimetric Methods (Exercises) 9.6: Gravimetric Methods (Summary) 4 https://chem.libretexts.org/@go/page/191312 10: Titrimetric Methods Titrimetry, in which volume serves as the analytical signal, made its first appearance as an analytical method in the early eighteenth century. Titrimetric methods were not well received by the analytical chemists of that era because they could not duplicate the accuracy and precision of a gravimetric analysis. Not surprisingly, few standard texts from the 1700s and 1800s include titrimetric methods of analysis. 10.1: Overview of Titrimetry 10.2: Acid–Base Titrations 10.3: Complexation Titrations 10.4: Redox Titrations 10.5: Precipitation Titrations 10.6: Titrimetric Methods (Exercises) 10.7: Titrimetric Methods (Summary) 11: Spectroscopic Methods "Colorimetry" is one example of a spectroscopic method of analysis. At the end of the nineteenth century, spectroscopy was limited to the absorption, emission, and scattering of visible, ultraviolet, and infrared electromagnetic radiation. Since its introduction, spectroscopy has expanded to include other forms of electromagnetic radiation—such as X-rays, microwaves, and radio waves—and other energetic particles—such as electrons and ions. 11.1: Overview of Spectroscopy 11.2: Spectroscopy Based on Absorption 11.03: UV 11.3: UV/Vis and IR Spectroscopy 11.4: Atomic Absorption Spectroscopy 11.5: Emission Spectroscopy 11.6: Photoluminescence Spectroscopy 11.7: Atomic Emission Spectroscopy 11.8: Spectroscopy Based on Scattering 11.9: Spectroscopic Methods (Exercises) 11.10: Spectroscopic Methods (Summary) 5 https://chem.libretexts.org/@go/page/191312 12: Electrochemical Methods In Chapter 10 we examined several spectroscopic techniques that take advantage of the interaction between electromagnetic radiation and matter. In this chapter we turn our attention to electrochemical techniques in which the potential, current, or charge in an electrochemical cell serves as the analytical signal. Although there are only three basic electrochemical signals, there are a many possible experimental designs—too many, in fact, to cover adequately in an introductory textbook. 12.1: Overview of Electrochemistry 12.2: Potentiometric Methods 12.3: Coulometric Methods 12.4: Voltammetric Methods 12.5: Electrochemical Methods (Exercises) 12.6: Electrochemical Methods (Summary) 13: Chromatographic For this reason, many analytical procedures include a step to separate the analyte from potential interferents. Although effective, each additional step in an analytical procedure increases the analysis time and introduces uncertainty. In this chapter we consider two analytical techniques that avoid these limitations by combining the separation and analysis: chromatography and electrophoresis. 13.1: Overview of Analytical Separations 13.2: General Theory of Column Chromatography 13.3: Optimizing Chromatographic Separations 13.4: Gas Chromatography 13.5: High-Performance Liquid Chromatography 13.6: Other Forms of Liquid Chromatography 13.7: Electrophoresis 13.8: Chromatographic and Electrophoretic Methods (Exercises) 13.9: Chromatographic and Electrophoretic Methods (Summary) 14: Kinetic Methods One way to classify analytical techniques is by whether the analyte’s concentration is determined by an equilibrium reaction or by the kinetics of a chemical reaction or a physical process. Often analytical methods involve measurements made on systems in which the analyte is always at equilibrium. In this chapter we turn our attention to measurements made under nonequilibrium conditions. 14.1: Kinetic Methods Versus Equilibrium Methods 14.2: Chemical Kinetics 14.3: Radiochemistry 14.4: Flow Injection Analysis 14.5: Kinetic Methods (Exercises) 14.6: Kinetic Methods (Summary) 6 https://chem.libretexts.org/@go/page/191312 15: Developing a Standard Method Among the goals of analytical chemistry are improving established methods of analysis, extending existing methods of analysis to new types of samples, and developing new analytical methods. In this chapter we discuss how we develop a standard method, including optimizing the experimental procedure, verifying that the method produces acceptable precision and accuracy in the hands of a single analyst, and validating the method for general use. 15.1: Optimizing the Experimental Procedure 15.2: Verifying the Method 15.3: Validating the Method as a Standard Method 15.4: Using Excel and R for an Analysis of Variance 15.5: Developing a Standard Method (Exercises) 15.6: Developing a Standard Method (Summary) 16: Quality Assurance Knowing that a method meets suitable standards is important if we are to have confidence in our results. Even so, using a standard method does not guarantee that the result of an analysis is acceptable. In this chapter we introduce the quality assurance procedures used in industry and government labs for monitoring routine chemical analyses. 16.1: The Analytical Perspective—Revisited 16.2: Quality Control 16.3: Quality Assessment 16.4: Evaluating Quality Assurance Data 16.5: Quality Assurance (Exercises) 17: Additional Resources 18: Back Matter Table of Contents 7 https://chem.libretexts.org/@go/page/191312 Index A alpha particle abbreviation 3.1: Measurements in Analytical Chemistry absorbance 4.3: Classifying Analytical Techniques 11.1: Overview of Spectroscopy 11.2: Spectroscopy Based on Absorption 15.1: Optimizing the Experimental Procedure Absorbance Spectra 11.2: Spectroscopy Based on Absorption absorbance spectrum 11.1: Overview of Spectroscopy Absorption 11.2: Spectroscopy Based on Absorption 11.6: Photoluminescence Spectroscopy absorption spectrophotometers 11.4: Atomic Absorption Spectroscopy absorption spectroscopy 11.2: Spectroscopy Based on Absorption 11.4: Atomic Absorption Spectroscopy absorption spectrum 13.5: High-Performance Liquid Chromatography absorptivity 11.2: Spectroscopy Based on Absorption 15.1: Optimizing the Experimental Procedure accuracy 4.4: Selecting an Analytical Method 5.2: Characterizing Experimental Errors 11.3: UV/Vis and IR Spectroscopy 11.4: Atomic Absorption Spectroscopy 11.7: Atomic Emission Spectroscopy 15.2: Verifying the Method 15.3: Validating the Method as a Standard Method acetic acid 7.6: Ladder Diagrams acid 7.4: Equilibrium Constants for Chemical Reactions 7.7: Solving Equilibrium Problems 7.8: Buffer Solutions acid–base buffer 7.8: Buffer Solutions acid–base titrations 10.2: Acid–Base Titrations acid–base titrimetry 10.2: Acid–Base Titrations 10.4: Redox Titrations acidity 10.2: Acid–Base Titrations activity 7.9: Activity Effects 12.2: Potentiometric Methods Activity Coefficients 7.9: Activity Effects Activity Effects 7.9: Activity Effects adjusted retention time 13.2: General Theory of Column Chromatography adsorption chromatography 13.1: Overview of Analytical Separations algorithm 15.1: Optimizing the Experimental Procedure Alkalinity 10.2: Acid–Base Titrations Analytical Columns 14.3: Radiochemistry 13.5: High-Performance Liquid Chromatography alternative hypotheses 5.5: Statistical Analysis of Data alternative hypothesis 5.5: Statistical Analysis of Data amalgam 12.4: Voltammetric Methods amperometry 12.1: Overview of Electrochemistry 12.4: Voltammetric Methods 13.5: High-Performance Liquid Chromatography amphiprotic 7.4: Equilibrium Constants for Chemical Reactions Amphiprotic Species 7.4: Equilibrium Constants for Chemical Reactions amplitude 11.1: Overview of Spectroscopy analysis 4.1: Analysis, Determination, and Measurement 14.1: Kinetic Methods Versus Equilibrium Methods Analysis of Standards 16.3: Quality Assessment Analysis of Variance 15.3: Validating the Method as a Standard Method 15.4: Using Excel and R for an Analysis of Variance analyst 15.2: Verifying the Method analysts 15.3: Validating the Method as a Standard Method analyte analytical data 16.1: The Analytical Perspective—Revisited analytical method 2.1: What is Analytical Chemistry? 4.4: Selecting an Analytical Method 5.5: Statistical Analysis of Data 6.1: Analytical Standards 6.3: Determining the Sensitivity 7.6: Ladder Diagrams 8.4: Separating the Analyte from Interferents 11.3: UV/Vis and IR Spectroscopy 15.3: Validating the Method as a Standard Method 16.4: Evaluating Quality Assurance Data analytical methodology 4.7: The Importance of Analytical Methodology analytical methods 4.4: Selecting an Analytical Method 4.7: The Importance of Analytical Methodology 6.5: Blank Corrections Analytical Perspective 16.1: The Analytical Perspective—Revisited analytical separation 8.5: General Theory of Separation Efficiency Analytical Separations 13.1: Overview of Analytical Separations analytical signal 9.1: Overview of Gravimetric Methods 13.5: High-Performance Liquid Chromatography 14.1: Kinetic Methods Versus Equilibrium Methods Analytical titrations 10.4: Redox Titrations 4.1: Analysis, Determination, and Measurement 8.5: General Theory of Separation Efficiency 9.2: Precipitation Gravimetry 9.4: Particulate Gravimetry 10.1: Overview of Titrimetry 11.3: UV/Vis and IR Spectroscopy 11.4: Atomic Absorption Spectroscopy 11.5: Emission Spectroscopy 12.1: Overview of Electrochemistry 12.2: Potentiometric Methods 12.3: Coulometric Methods 13.1: Overview of Analytical Separations 13.4: Gas Chromatography 15.1: Optimizing the Experimental Procedure 16.3: Quality Assessment Analyte’s Concentration 13.4: Gas Chromatography analytes Analyze Data 5.8: Using Excel and R to Analyze Data anodic current 12.4: Voltammetric Methods anova 15.3: Validating the Method as a Standard Method Applied Potential 12.4: Voltammetric Methods aqueous buffer 13.7: Electrophoresis argentometric titration 10.5: Precipitation Titrations asymmetric equivalence point 10.4: Redox Titrations Asymmetric Peaks 11.6: Photoluminescence Spectroscopy 13.7: Electrophoresis analytical 14.1: Kinetic Methods Versus Equilibrium Methods Analytical Approach 2.2: The Analytical Perspective analytical balance 13.2: General Theory of Column Chromatography Atomic emission 11.7: Atomic Emission Spectroscopy Atomic Emission Spectra 11.7: Atomic Emission Spectroscopy Atomic Emission Spectroscopy 11.7: Atomic Emission Spectroscopy 3.4: Basic Equipment analytical calculations 3.3: Stoichiometric Calculations analytical chemistry 2.1: What is Analytical Chemistry? 3.1: Measurements in Analytical Chemistry 12.1: Overview of Electrochemistry analytical chemists 2.2: The Analytical Perspective 1 atomic number 14.3: Radiochemistry Atomization 11.4: Atomic Absorption Spectroscopy 11.7: Atomic Emission Spectroscopy Atomization Methods 11.4: Atomic Absorption Spectroscopy attenuated total reflectance 11.3: UV/Vis and IR Spectroscopy https://chem.libretexts.org/@go/page/211867 auxiliary complexing agent 10.3: Complexation Titrations auxiliary electrode 12.1: Overview of Electrochemistry 13.5: High-Performance Liquid Chromatography auxiliary oxidizing agents 10.4: Redox Titrations auxiliary reducing agent 10.4: Redox Titrations average 5.6: Statistical Methods for Normal Distributions calomel electrodes chemical analysis 12.2: Potentiometric Methods capillary 13.5: High-Performance Liquid Chromatography 13.7: Electrophoresis Capillary Columns capillary electrochromatography 13.7: Electrophoresis Capillary Electrophoresis capillary gel electrophoresis background correction 11.4: Atomic Absorption Spectroscopy balanced reaction 3.3: Stoichiometric Calculations band broadening 13.2: General Theory of Column Chromatography base 7.4: Equilibrium Constants for Chemical Reactions baseline width 13.2: General Theory of Column Chromatography Beer’s Law 11.2: Spectroscopy Based on Absorption Berthollet 7.1: Reversible Reactions and Chemical Equilibria beta particle 14.3: Radiochemistry binomial distribution 5.4: The Distribution of Measurements and Results blank 6.5: Blank Corrections blind analysis 15.2: Verifying the Method Bonded stationary phases 13.5: High-Performance Liquid Chromatography box plot 5.8: Using Excel and R to Analyze Data buffer 7.8: Buffer Solutions 13.7: Electrophoresis buffer capacity 7.8: Buffer Solutions Buffer Solutions 7.8: Buffer Solutions buffer viscosity 13.7: Electrophoresis Buret 10.1: Overview of Titrimetry C calculations 3.3: Stoichiometric Calculations Calibration 4.5: Developing the Procedure calibration curve 14.2: Chemical Kinetics 15.1: Optimizing the Experimental Procedure Calibration Curves 6.4: Linear Regression and Calibration Curves Calomel 12.2: Potentiometric Methods 11.4: Atomic Absorption Spectroscopy 11.7: Atomic Emission Spectroscopy Chemical kinetic 13.3: Optimizing Chromatographic Separations 13.4: Gas Chromatography 13.7: Electrophoresis B 2.1: What is Analytical Chemistry? Chemical Interferences 13.7: Electrophoresis 14.2: Chemical Kinetics 14.4: Flow Injection Analysis Chemical kinetic methods 14.2: Chemical Kinetics 14.4: Flow Injection Analysis chemical kinetics 14.2: Chemical Kinetics Chemical Properties 8.6: Classifying Separation Techniques capillary tubing chemical reaction 13.7: Electrophoresis Capillary Zone Electrophoresis 13.7: Electrophoresis 7.2: Thermodynamics and Equilibrium Chemistry 14.2: Chemical Kinetics chemiluminescence capillary’s radius 11.1: Overview of Spectroscopy 13.7: Electrophoresis Chesapeake Bay Monitoring Program Catalytic activity 4.7: The Importance of Analytical Methodology 14.2: Chemical Kinetics chromatogram cathode 12.2: Potentiometric Methods cathodic current 12.4: Voltammetric Methods CCB 13.4: Gas Chromatography Chromatographic 13.2: General Theory of Column Chromatography Chromatographic Columns 13.4: Gas Chromatography 4.6: Protocols Chromatographic Resolution CCV 13.2: General Theory of Column Chromatography 4.6: Protocols chromatography CEC 13.7: Electrophoresis central composite design 15.1: Optimizing the Experimental Procedure Central Limit Theorem 5.4: The Distribution of Measurements and Results Central Tendency 5.1: Characterizing Measurements and Results centrifugal analyzer 8.6: Classifying Separation Techniques 13.1: Overview of Analytical Separations 13.2: General Theory of Column Chromatography 13.4: Gas Chromatography 13.5: High-Performance Liquid Chromatography 13.6: Other Forms of Liquid Chromatography Claude Berthollet 7.1: Reversible Reactions and Chemical Equilibria Clinical 11.3: UV/Vis and IR Spectroscopy 14.2: Chemical Kinetics coagulation centrifugation 8.6: Classifying Separation Techniques CGE 9.2: Precipitation Gravimetry Collaborative Study 15.3: Validating the Method as a Standard Method 13.7: Electrophoresis collaborative test characteristic decay 15.3: Validating the Method as a Standard Method 14.3: Radiochemistry Collaborative Testing Characterization 10.2: Acid–Base Titrations 11.3: UV/Vis and IR Spectroscopy 12.3: Coulometric Methods 12.4: Voltammetric Methods 14.2: Chemical Kinetics 14.3: Radiochemistry characterization analysis 2.3: Common Analytical Problems charge 12.3: Coulometric Methods charge balance 15.3: Validating the Method as a Standard Method column 13.6: Other Forms of Liquid Chromatography column chromatography 13.1: Overview of Analytical Separations 13.2: General Theory of Column Chromatography column efficiency 13.2: General Theory of Column Chromatography 13.3: Optimizing Chromatographic Separations Columns 13.5: High-Performance Liquid Chromatography 7.7: Solving Equilibrium Problems charge balance equation 7.7: Solving Equilibrium Problems charging current common ion effect 7.7: Solving Equilibrium Problems competitive inhibition 14.2: Chemical Kinetics 12.4: Voltammetric Methods Chauvenet’s criterion 5.6: Statistical Methods for Normal Distributions 2 Complexation 7.4: Equilibrium Constants for Chemical Reactions 7.6: Ladder Diagrams https://chem.libretexts.org/@go/page/211867 Complexation Reactions convection 7.4: Equilibrium Constants for Chemical Reactions complexation titrations 10.3: Complexation Titrations Complexation Titrimetry 10.3: Complexation Titrations composite sample 8.2: Designing a Sampling Plan concentration 3.2: Concentration 3.4: Basic Equipment 5.7: Detection Limits 6.4: Linear Regression and Calibration Curves 7.7: Solving Equilibrium Problems 7.9: Activity Effects 7.10: Using Excel and R to Solve Equilibrium Problems 8.5: General Theory of Separation Efficiency 9.2: Precipitation Gravimetry 10.2: Acid–Base Titrations 11.8: Spectroscopy Based on Scattering 12.2: Potentiometric Methods 12.3: Coulometric Methods 12.4: Voltammetric Methods 13.1: Overview of Analytical Separations 13.4: Gas Chromatography 13.7: Electrophoresis 14.2: Chemical Kinetics 14.4: Flow Injection Analysis 15.1: Optimizing the Experimental Procedure 15.2: Verifying the Method 16.3: Quality Assessment convenience sampling 8.2: Designing a Sampling Plan coprecipitates 9.2: Precipitation Gravimetry corresponding 7.8: Buffer Solutions 14.4: Flow Injection Analysis 4.3: Classifying Analytical Techniques concentrations 10.2: Acid–Base Titrations 10.4: Redox Titrations 12.1: Overview of Electrochemistry 16.4: Evaluating Quality Assurance Data 4.4: Selecting an Analytical Method coulombs 12.3: Coulometric Methods coulometric titration 12.3: Coulometric Methods Coulometric Titrations 12.3: Coulometric Methods coulometry 12.3: Coulometric Methods 13.5: High-Performance Liquid Chromatography counter electrode 12.1: Overview of Electrochemistry countercurrent extraction 13.1: Overview of Analytical Separations cryogenic focusing 13.4: Gas Chromatography Current 12.1: Overview of Electrochemistry 12.4: Voltammetric Methods Current efficiency 10.3: Complexation Titrations conductivity 13.5: High-Performance Liquid Chromatography Confidence Interval 5.5: Statistical Analysis of Data 15.3: Validating the Method as a Standard Method Confidence Intervals 5.4: The Distribution of Measurements and Results coning 8.3: Implementing the Sampling Plan conservation of mass 9.1: Overview of Gravimetric Methods constant determinate error 5.2: Characterizing Experimental Errors Constant Potential 12.3: Coulometric Methods continuing calibration blank 4.6: Protocols continuing calibration verification 4.6: Protocols contour map 15.1: Optimizing the Experimental Procedure Contract Laboratory Program 4.6: Protocols control chart 16.4: Evaluating Quality Assurance Data 15.2: Verifying the Method detection limit 4.4: Selecting an Analytical Method 5.7: Detection Limits 15.2: Verifying the Method 16.4: Evaluating Quality Assurance Data 14.4: Flow Injection Analysis Detectors 13.5: High-Performance Liquid Chromatography 13.7: Electrophoresis determinate error 5.2: Characterizing Experimental Errors Determination 4.1: Analysis, Determination, and Measurement 5.4: The Distribution of Measurements and Results Dialysis 8.6: Classifying Separation Techniques 14.4: Flow Injection Analysis diffusion 12.4: Voltammetric Methods 14.4: Flow Injection Analysis diffusion layer 12.4: Voltammetric Methods Digestion 9.2: Precipitation Gravimetry dilution 3.5: Preparing Solutions 12.3: Coulometric Methods curve fitting Diode Array Spectrometer 11.3: UV/Vis and IR Spectroscopy 14.2: Chemical Kinetics Curvilinear regression 6.4: Linear Regression and Calibration Curves Cyclic Voltammetry direct analysis 9.1: Overview of Gravimetric Methods direct titration 10.1: Overview of Titrimetry 12.4: Voltammetric Methods conditional formation constant 3.4: Basic Equipment detection Detector Cost concentration gradient concentration techniques desiccator 12.4: Voltammetric Methods 14.4: Flow Injection Analysis dispersion 14.4: Flow Injection Analysis D displacement titration dark current 10.1: Overview of Titrimetry 11.1: Overview of Spectroscopy Data 5.5: Statistical Analysis of Data 5.8: Using Excel and R to Analyze Data Data Analysis 5.8: Using Excel and R to Analyze Data 6.6: Using Excel and R for a Regression Analysis 15.4: Using Excel and R for an Analysis of Variance definitive techniques 9.1: Overview of Gravimetric Methods degrees of freedom 5.4: The Distribution of Measurements and Results 15.3: Validating the Method as a Standard Method density 8.6: Classifying Separation Techniques density gradient centrifugation 8.6: Classifying Separation Techniques dependent 15.1: Optimizing the Experimental Procedure dependent factors 15.1: Optimizing the Experimental Procedure Descriptive Statistics 5.8: Using Excel and R to Analyze Data desiccant dissociation 7.4: Equilibrium Constants for Chemical Reactions 7.8: Buffer Solutions dissociation constant 7.4: Equilibrium Constants for Chemical Reactions 7.8: Buffer Solutions distillation 8.6: Classifying Separation Techniques Distribution of Measurements 5.4: The Distribution of Measurements and Results Distribution Ratios 8.7: Liquid–Liquid Extractions Dixon’s Q‑test 5.6: Statistical Methods for Normal Distributions DME 12.4: Voltammetric Methods dot chart 5.8: Using Excel and R to Analyze Data dropping mercury electrode 12.4: Voltammetric Methods Drying 3.4: Basic Equipment duplicate samples 16.3: Quality Assessment 3.4: Basic Equipment 3 https://chem.libretexts.org/@go/page/211867 E electroosmotic flow velocity ECD 13.4: Gas Chromatography EDTA 10.3: Complexation Titrations effective 15.1: Optimizing the Experimental Procedure effective bandwidth 11.1: Overview of Spectroscopy effective electric 13.7: Electrophoresis effective electric field 13.7: Electrophoresis effectiveness 15.1: Optimizing the Experimental Procedure Efficiency 13.7: Electrophoresis 15.1: Optimizing the Experimental Procedure electrochemical cell 12.3: Coulometric Methods 12.4: Voltammetric Methods electrochemical cells 12.2: Potentiometric Methods Electrochemical Detectors 13.5: High-Performance Liquid Chromatography electrochemical measurements 13.5: High-Performance Liquid Chromatography Electrochemical Techniques 12.1: Overview of Electrochemistry electrochemically irreversible 12.4: Voltammetric Methods electrochemically reversible 12.4: Voltammetric Methods electrochemistry 4.3: Classifying Analytical Techniques 12.1: Overview of Electrochemistry electrode 12.1: Overview of Electrochemistry 12.2: Potentiometric Methods 12.3: Coulometric Methods electrode’s potential 12.3: Coulometric Methods electrodes 12.2: Potentiometric Methods Electrogravimetry 9.1: Overview of Gravimetric Methods 12.3: Coulometric Methods electrokinetic injection 13.7: Electrophoresis electrolysis 12.3: Coulometric Methods Electrolysis Time 12.3: Coulometric Methods electromagnetic radiation 11.1: Overview of Spectroscopy 11.2: Spectroscopy Based on Absorption 15.1: Optimizing the Experimental Procedure electromagnetic spectrum 11.1: Overview of Spectroscopy electron capture detector 13.4: Gas Chromatography electroosmotic 13.7: Electrophoresis electroosmotic flow 13.7: Electrophoresis equilibrium constan 7.3: Manipulating Equilibrium Constants electropherogram equilibrium constant 13.7: Electrophoresis 7.2: Thermodynamics and Equilibrium Chemistry 7.3: Manipulating Equilibrium Constants 12.2: Potentiometric Methods electrophoresis 13.7: Electrophoresis Equilibrium Constants Electrophoretic 13.1: Overview of Analytical Separations Electrophoretic Mobility 13.7: Electrophoresis Electrophoretic Separations 13.1: Overview of Analytical Separations electrophoretic velocity 13.7: Electrophoresis 7.3: Manipulating Equilibrium Constants 10.2: Acid–Base Titrations 11.3: UV/Vis and IR Spectroscopy equilibrium method 14.1: Kinetic Methods Versus Equilibrium Methods equilibrium reaction 8.7: Liquid–Liquid Extractions 14.1: Kinetic Methods Versus Equilibrium Methods Equipment emission 11.1: Overview of Spectroscopy 14.3: Radiochemistry emission spectra 11.6: Photoluminescence Spectroscopy 11.7: Atomic Emission Spectroscopy Emission Spectroscopy 11.7: Atomic Emission Spectroscopy emission spectrum 11.6: Photoluminescence Spectroscopy empirical model 15.1: Optimizing the Experimental Procedure End point 10.2: Acid–Base Titrations 10.3: Complexation Titrations 10.5: Precipitation Titrations End points 10.1: Overview of Titrimetry Endpoint 12.3: Coulometric Methods enthalpy 7.2: Thermodynamics and Equilibrium Chemistry entropy 7.2: Thermodynamics and Equilibrium Chemistry environmental monitoring programs 4.7: The Importance of Analytical Methodology Enzyme Catalysis 14.2: Chemical Kinetics enzyme electrodes 12.2: Potentiometric Methods Enzymes 4.4: Selecting an Analytical Method equivalence 10.1: Overview of Titrimetry 10.2: Acid–Base Titrations equivalence point 10.1: Overview of Titrimetry 10.2: Acid–Base Titrations 10.4: Redox Titrations Equivalence Points 10.1: Overview of Titrimetry Equivalency Testing 15.2: Verifying the Method Equivalent Weights 10.2: Acid–Base Titrations error 5.2: Characterizing Experimental Errors 15.3: Validating the Method as a Standard Method errors 16.4: Evaluating Quality Assurance Data Ethylenediaminetetraacetic 10.3: Complexation Titrations ethylenediaminetetraacetic acid 10.3: Complexation Titrations Excel 3.6: Spreadsheets and Computational Software 5.8: Using Excel and R to Analyze Data 6.6: Using Excel and R for a Regression Analysis 15.4: Using Excel and R for an Analysis of Variance Excitation 11.2: Spectroscopy Based on Absorption 11.7: Atomic Emission Spectroscopy excitation spectrum 14.2: Chemical Kinetics Equilibria 11.6: Photoluminescence Spectroscopy exclusion limit 7.6: Ladder Diagrams equilibrium 13.6: Other Forms of Liquid Chromatography 7.1: Reversible Reactions and Chemical Equilibria 7.3: Manipulating Equilibrium Constants 7.5: Le Châtelier’s Principle 7.6: Ladder Diagrams 7.7: Solving Equilibrium Problems 7.9: Activity Effects 7.10: Using Excel and R to Solve Equilibrium Problems 8.7: Liquid–Liquid Extractions 11.3: UV/Vis and IR Spectroscopy 12.1: Overview of Electrochemistry equilibrium chemistry 7.6: Ladder Diagrams equilibrium concentration Experimental Errors 5.2: Characterizing Experimental Errors external conversion 11.6: Photoluminescence Spectroscopy External Standards 6.3: Determining the Sensitivity 12.2: Potentiometric Methods extraction 8.6: Classifying Separation Techniques 8.7: Liquid–Liquid Extractions Extraction efficiency 8.7: Liquid–Liquid Extractions 7.7: Solving Equilibrium Problems 7.10: Using Excel and R to Solve Equilibrium Problems 13.7: Electrophoresis 4 https://chem.libretexts.org/@go/page/211867 F Fourier transform spectrometer factor levels 15.1: Optimizing the Experimental Procedure Factorial 15.1: Optimizing the Experimental Procedure Factorial Designs 15.1: Optimizing the Experimental Procedure factors 15.1: Optimizing the Experimental Procedure 15.2: Verifying the Method Fajans method 10.5: Precipitation Titrations faradaic current 12.4: Voltammetric Methods Faraday’s constant 12.3: Coulometric Methods Faraday’s law 12.3: Coulometric Methods fiagram 14.4: Flow Injection Analysis FID 13.4: Gas Chromatography field blank 16.3: Quality Assessment 16.4: Evaluating Quality Assurance Data filter 11.1: Overview of Spectroscopy Filter Photometer 11.3: UV/Vis and IR Spectroscopy filtrate 8.6: Classifying Separation Techniques filtration 8.6: Classifying Separation Techniques Flame Atomizer 11.4: Atomic Absorption Spectroscopy Flame Ionization Detector 13.4: Gas Chromatography flow injection 14.4: Flow Injection Analysis flow injection analysis 14.4: Flow Injection Analysis flow injection analyzer 14.4: Flow Injection Analysis fluorescence 11.6: Photoluminescence Spectroscopy Fluorescence spectra 11.6: Photoluminescence Spectroscopy fluorescent 11.6: Photoluminescence Spectroscopy 13.5: High-Performance Liquid Chromatography fluorescent quantum yield 11.6: Photoluminescence Spectroscopy fluorimeter 11.6: Photoluminescence Spectroscopy Forensic 11.3: UV/Vis and IR Spectroscopy formality 3.2: Concentration formation constant 7.4: Equilibrium Constants for Chemical Reactions 14.1: Kinetic Methods Versus Equilibrium Methods Gravimetry 11.3: UV/Vis and IR Spectroscopy 4.3: Classifying Analytical Techniques 9: Gravimetric Methods 9.1: Overview of Gravimetric Methods 9.2: Precipitation Gravimetry 9.3: Volatilization Gravimetry 9.4: Particulate Gravimetry frequency 11.1: Overview of Spectroscopy fundamental analysis 2.3: Common Analytical Problems G gross sample 8.3: Implementing the Sampling Plan Grubb’s test galvanostat 12.1: Overview of Electrochemistry Galvanostats 12.1: Overview of Electrochemistry gamma ray 5.6: Statistical Methods for Normal Distributions GSC 13.4: Gas Chromatography Guard columns 13.5: High-Performance Liquid Chromatography 14.3: Radiochemistry gas 8.3: Implementing the Sampling Plan 13.4: Gas Chromatography gas chromatography H hanging mercury drop electrode 12.4: Voltammetric Methods 13.3: Optimizing Chromatographic Separations 13.4: Gas Chromatography Gas–Liquid Chromatography 13.4: Gas Chromatography gaseous diffusion 14.4: Flow Injection Analysis Gases 8.3: Implementing the Sampling Plan Gaussian 13.2: General Theory of Column Chromatography GC detectors 13.6: Other Forms of Liquid Chromatography Geiger counter headspace sampling 13.4: Gas Chromatography Henderson–Hasselbalch approximation 7.8: Buffer Solutions heterogeneous 8.2: Designing a Sampling Plan histogram 5.4: The Distribution of Measurements and Results HMDE 12.4: Voltammetric Methods homogeneous 8.2: Designing a Sampling Plan homogeneous precipitation 14.3: Radiochemistry general elution problem 13.3: Optimizing Chromatographic Separations Gibb’s free energy 7.2: Thermodynamics and Equilibrium Chemistry glass electrodes 12.2: Potentiometric Methods GLC 13.4: Gas Chromatography global optimum 15.1: Optimizing the Experimental Procedure GMP 9.2: Precipitation Gravimetry HPLC 13.5: High-Performance Liquid Chromatography HPLC column 13.6: Other Forms of Liquid Chromatography HPLC detectors 13.5: High-Performance Liquid Chromatography HPLC Plumbing 13.5: High-Performance Liquid Chromatography Hydrodynamic injection 13.7: Electrophoresis hydrodynamic voltammetry 16.2: Quality Control 12.4: Voltammetric Methods GMPs 16.2: Quality Control Good laboratory practices 16.2: Quality Control Good measurement practices 16.2: Quality Control I ICB 4.6: Protocols ICV 4.6: Protocols grab sample 8.2: Designing a Sampling Plan gradient elutions 13.5: High-Performance Liquid Chromatography graphite furnace 11.4: Atomic Absorption Spectroscopy gravimetric analysis ICV and 4.6: Protocols ignition 9.2: Precipitation Gravimetry Ilkovic equation 12.4: Voltammetric Methods In situ sampling 9: Gravimetric Methods 8.2: Designing a Sampling Plan gravimetric method 4.4: Selecting an Analytical Method Incident Radiation 11.8: Spectroscopy Based on Scattering inclusion Formation constants 9.2: Precipitation Gravimetry 10.3: Complexation Titrations 5 https://chem.libretexts.org/@go/page/211867 inclusion limit IR Spectroscopy 13.6: Other Forms of Liquid Chromatography Independent isocratic elution 15.1: Optimizing the Experimental Procedure independent factors 13.5: High-Performance Liquid Chromatography 10.1: Overview of Titrimetry 10.2: Acid–Base Titrations 10.5: Precipitation Titrations 12.2: Potentiometric Methods indicator electrode 12.1: Overview of Electrochemistry Indicator Electrodes 12.2: Potentiometric Methods indirect analysis 9.1: Overview of Gravimetric Methods Infrared Spectra 11.2: Spectroscopy Based on Absorption inhibitor 13.4: Gas Chromatography initial calibration blank 4.6: Protocols initial calibration verification 14.3: Radiochemistry 14.3: Radiochemistry 14.2: Chemical Kinetics 9.3: Volatilization Gravimetry Instrumentation 11.3: UV/Vis and IR Spectroscopy 11.6: Photoluminescence Spectroscopy 12.3: Coulometric Methods 14.3: Radiochemistry 14.4: Flow Injection Analysis integrated rate law 14.2: Chemical Kinetics 12.1: Overview of Electrochemistry 12.1: Overview of Electrochemistry Interferences 4.5: Developing the Procedure interferent 4.4: Selecting an Analytical Method interferogram 11.1: Overview of Spectroscopy interferometer 11.1: Overview of Spectroscopy Interferometers 11.1: Overview of Spectroscopy internal conversion 11.6: Photoluminescence Spectroscopy internal standard 6.3: Determining the Sensitivity intersystem crossing 11.6: Photoluminescence Spectroscopy ionic strength 7.9: Activity Effects ionization suppressor 11.4: Atomic Absorption Spectroscopy IR spectra 11.2: Spectroscopy Based on Absorption 13.1: Overview of Analytical Separations liquid–solid adsorption chromatography J 13.6: Other Forms of Liquid Chromatography local optimum Jones reductor 15.1: Optimizing the Experimental Procedure 10.4: Redox Titrations longitudinal diffusion Joule heating 13.3: Optimizing Chromatographic Separations 13.7: Electrophoresis judgmental sampling 8.2: Designing a Sampling Plan junction potential 12.2: Potentiometric Methods loop injector 13.5: High-Performance Liquid Chromatography LSC 13.6: Other Forms of Liquid Chromatography M K manifold Ka 4.4: Selecting an Analytical Method 6.4: Linear Regression and Calibration Curves 7.4: Equilibrium Constants for Chemical Reactions Kb 7.4: Equilibrium Constants for Chemical Reactions KD 8.6: Classifying Separation Techniques kernel density plot 5.8: Using Excel and R to Analyze Data kinetic method 14.1: Kinetic Methods Versus Equilibrium Methods Kjeldahl analysis 10.2: Acid–Base Titrations Interfacial Interfacial Concentrations 13.5: High-Performance Liquid Chromatography Liquid–Liquid Extractions 5.7: Detection Limits initial rate Inorganic Analysis 13.5: High-Performance Liquid Chromatography liquid mobile phase IUPAC 4.6: Protocols 6.4: Linear Regression and Calibration Curves liquid chromatography isotopes 14.2: Chemical Kinetics 12.4: Voltammetric Methods Linear Regression isotope dilution 5.2: Characterizing Experimental Errors indicator 5.7: Detection Limits limiting current isothermal 15.1: Optimizing the Experimental Procedure indeterminate errors limit of identification 11.3: UV/Vis and IR Spectroscopy 14.4: Flow Injection Analysis mass 3.4: Basic Equipment 4.3: Classifying Analytical Techniques 5.1: Characterizing Measurements and Results 8.6: Classifying Separation Techniques 9.1: Overview of Gravimetric Methods mass spectrometer 13.4: Gas Chromatography mass spectrum 13.4: Gas Chromatography Mass Transfer 13.3: Optimizing Chromatographic Separations mass transport 12.4: Voltammetric Methods L Mathematical laboratory 3.7: The Laboratory Notebook laboratory notebook 3.7: The Laboratory Notebook laboratory sample 8.3: Implementing the Sampling Plan Ladder diagram 7.6: Ladder Diagrams 12.3: Coulometric Methods Ladder diagrams 7.8: Buffer Solutions laminar flow 15.1: Optimizing the Experimental Procedure Mathematical Models 15.1: Optimizing the Experimental Procedure matrix 4.1: Analysis, Determination, and Measurement matrix matching 6.3: Determining the Sensitivity mean 5.1: Characterizing Measurements and Results 5.6: Statistical Methods for Normal Distributions 15.3: Validating the Method as a Standard Method measurement 14.4: Flow Injection Analysis Le Châtelier’s principle 7.5: Le Châtelier’s Principle 7.6: Ladder Diagrams Le Chatelier's Principle 7.5: Le Châtelier’s Principle leveling 10.2: Acid–Base Titrations lifetime 11.5: Emission Spectroscopy ligand 4.1: Analysis, Determination, and Measurement 5.1: Characterizing Measurements and Results 5.2: Characterizing Experimental Errors Measurement Errors 5.2: Characterizing Experimental Errors measurements 3.1: Measurements in Analytical Chemistry 5.4: The Distribution of Measurements and Results 12.2: Potentiometric Methods 15.1: Optimizing the Experimental Procedure Measuring Volume 3.4: Basic Equipment 7.4: Equilibrium Constants for Chemical Reactions 6 https://chem.libretexts.org/@go/page/211867 median molarity 5.1: Characterizing Measurements and Results medication normality 3.2: Concentration 3.2: Concentration Moles 5.5: Statistical Analysis of Data notebook 3.3: Stoichiometric Calculations MEKC Monitoring Absorbance 13.7: Electrophoresis 3.7: The Laboratory Notebook Nuclear Reactor 10.3: Complexation Titrations Membrane Electrodes monitoring program 12.2: Potentiometric Methods 14.3: Radiochemistry Nyquist theorem 4.7: The Importance of Analytical Methodology membrane potential monochromatic 12.2: Potentiometric Methods 11.1: Overview of Spectroscopy 11.8: Spectroscopy Based on Scattering Membrane Potentials monochromator 12.2: Potentiometric Methods 11.1: Overview of Spectroscopy Membranes Monolithic columns 12.2: Potentiometric Methods 13.5: High-Performance Liquid Chromatography meniscus Monoprotic 3.4: Basic Equipment 7.4: Equilibrium Constants for Chemical Reactions 7.7: Solving Equilibrium Problems mercury film electrode 12.4: Voltammetric Methods MS metallochromic indicators 13.4: Gas Chromatography 10.3: Complexation Titrations Multicomponent Analysis method 4.2: Techniques, Methods, Procedures, and Protocols 4.4: Selecting an Analytical Method 6.3: Determining the Sensitivity method blank 12.4: Voltammetric Methods Multielemental Analysis 11.7: Atomic Emission Spectroscopy multiple paths 4.5: Developing the Procedure 16.3: Quality Assessment 13.3: Optimizing Chromatographic Separations Multivariate Regression method error 6.4: Linear Regression and Calibration Curves 8.2: Designing a Sampling Plan O Occlusions 9.2: Precipitation Gravimetry Ohm’s law 12.1: Overview of Electrochemistry open tubular column 13.4: Gas Chromatography Optimization 15.1: Optimizing the Experimental Procedure Optimize Resolution 13.3: Optimizing Chromatographic Separations Organic Analysis 9.3: Volatilization Gravimetry Outliers 5.6: Statistical Methods for Normal Distributions overpotential 12.3: Coulometric Methods oxidation 7.4: Equilibrium Constants for Chemical Reactions 7.6: Ladder Diagrams 5.2: Characterizing Experimental Errors Method Errors N 5.2: Characterizing Experimental Errors method of continuous variations 12.2: Potentiometric Methods 14.3: Radiochemistry 11.3: UV/Vis and IR Spectroscopy oxidizing agent Nephelometry method of standard additions 7.4: Equilibrium Constants for Chemical Reactions 11.8: Spectroscopy Based on Scattering 6.3: Determining the Sensitivity Micellar electrokinetic chromatography oxidation reaction negatron capillary 13.7: Electrophoresis Micelle 13.7: Electrophoresis Michaelis constant 14.2: Chemical Kinetics microextraction 13.4: Gas Chromatography Microsoft Excel 3.6: Spreadsheets and Computational Software migration 12.4: Voltammetric Methods Migration Time 13.7: Electrophoresis mobile phase 13.1: Overview of Analytical Separations 13.4: Gas Chromatography 13.5: High-Performance Liquid Chromatography 13.6: Other Forms of Liquid Chromatography Mobile Phases 13.1: Overview of Analytical Separations Mobility 13.7: Electrophoresis Mohr method 10.5: Precipitation Titrations molar absorptivity 11.2: Spectroscopy Based on Absorption 15.1: Optimizing the Experimental Procedure Nernst Equation 7.4: Equilibrium Constants for Chemical Reactions 12.2: Potentiometric Methods Nessler 11.1: Overview of Spectroscopy neutron P Packed columns 13.4: Gas Chromatography paired data 5.6: Statistical Methods for Normal Distributions Participate 14.3: Radiochemistry 12.1: Overview of Electrochemistry neutron activation Particulate gravimetry 14.3: Radiochemistry Neutron Activation Analysis 14.3: Radiochemistry 9.1: Overview of Gravimetric Methods 9.4: Particulate Gravimetry particulates neutron flux 9.4: Particulate Gravimetry 14.3: Radiochemistry partition coefficient nominal wavelength 11.1: Overview of Spectroscopy Noncatalytic Reactions 14.2: Chemical Kinetics Noncompetitive Inhibition 14.2: Chemical Kinetics 8.6: Classifying Separation Techniques Partition Coefficients 8.7: Liquid–Liquid Extractions parts per billion 3.2: Concentration Parts per million nonfaradaic current 12.4: Voltammetric Methods nonretained solutes 13.2: General Theory of Column Chromatography normal calibration curve 6.3: Determining the Sensitivity normal distribution 5.4: The Distribution of Measurements and Results 5.5: Statistical Analysis of Data 5.6: Statistical Methods for Normal Distributions Normal Distributions 5.6: Statistical Methods for Normal Distributions 7 3.2: Concentration pathlength 15.1: Optimizing the Experimental Procedure peak capacity 13.2: General Theory of Column Chromatography peak current 12.4: Voltammetric Methods Peak height 14.4: Flow Injection Analysis peak shape 13.2: General Theory of Column Chromatography https://chem.libretexts.org/@go/page/211867 peptization 9.2: Precipitation Gravimetry personal error 5.2: Characterizing Experimental Errors pH 7.4: Equilibrium Constants for Chemical Reactions 7.10: Using Excel and R to Solve Equilibrium Problems 10.2: Acid–Base Titrations 12.2: Potentiometric Methods pH scale 7.4: Equilibrium Constants for Chemical Reactions phase angle 11.1: Overview of Spectroscopy phosphorescence 11.6: Photoluminescence Spectroscopy Phosphorescence Spectra 11.6: Photoluminescence Spectroscopy phosphorescent 11.6: Photoluminescence Spectroscopy phosphorescent quantum yield 11.6: Photoluminescence Spectroscopy photodiode array 11.1: Overview of Spectroscopy Photoluminescence 11.1: Overview of Spectroscopy 11.5: Emission Spectroscopy 11.6: Photoluminescence Spectroscopy Photoluminescence spectroscopy 11.6: Photoluminescence Spectroscopy photon 11.1: Overview of Spectroscopy 11.2: Spectroscopy Based on Absorption Photon Transducers 11.1: Overview of Spectroscopy photons 11.1: Overview of Spectroscopy physical properties 8.6: Classifying Separation Techniques pipet 3.4: Basic Equipment planar chromatography 13.1: Overview of Analytical Separations plasma 11.7: Atomic Emission Spectroscopy PLOT 6.6: Using Excel and R for a Regression Analysis 13.4: Gas Chromatography Plumbing 13.5: High-Performance Liquid Chromatography pnorm 5.8: Using Excel and R to Analyze Data point 10.2: Acid–Base Titrations polarity index 13.5: High-Performance Liquid Chromatography polarography 12.4: Voltammetric Methods polychromatic 11.1: Overview of Spectroscopy Polyprotic 7.4: Equilibrium Constants for Chemical Reactions 7.7: Solving Equilibrium Problems population Preconcentration 5.4: The Distribution of Measurements and Results 8.1: The Importance of Sampling 8.2: Designing a Sampling Plan Populations 5.4: The Distribution of Measurements and Results Positron 8.8: Separation Versus Preconcentration Prescriptive Approach 16.4: Evaluating Quality Assurance Data pressure 7.2: Thermodynamics and Equilibrium Chemistry primary standard 14.3: Radiochemistry 6.1: Analytical Standards potential 12.1: Overview of Electrochemistry 12.2: Potentiometric Methods 12.4: Voltammetric Methods potential interferents 13.1: Overview of Analytical Separations potentiometer 12.1: Overview of Electrochemistry Potentiometric 12.2: Potentiometric Methods Potentiometric Biosensors 12.2: Potentiometric Methods Potentiometric Measurements 12.2: Potentiometric Methods potentiometric method 12.3: Coulometric Methods Potentiometric Methods 12.2: Potentiometric Methods potentiometric titration curve 10.2: Acid–Base Titrations potentiometry 12.2: Potentiometric Methods potentiostat 12.1: Overview of Electrochemistry Potentiostats 12.1: Overview of Electrochemistry ppb Probability Distributions 5.4: The Distribution of Measurements and Results 5.8: Using Excel and R to Analyze Data procedure 4.2: Techniques, Methods, Procedures, and Protocols product 7.5: Le Châtelier’s Principle products 3.3: Stoichiometric Calculations 7.5: Le Châtelier’s Principle proficiency standards 16.3: Quality Assessment propagation of uncertainty 5.3: Propagation of Uncertainty Property Control Chart 16.4: Evaluating Quality Assurance Data proportional determinate error 5.2: Characterizing Experimental Errors protocol 4.2: Techniques, Methods, Procedures, and Protocols protocol for a specific purpose 16.2: Quality Control proton 14.3: Radiochemistry PSP 16.2: Quality Control pulse polarography 3.2: Concentration 12.4: Voltammetric Methods ppm 3.2: Concentration Q precipitant 9.2: Precipitation Gravimetry precipitate 7.4: Equilibrium Constants for Chemical Reactions 9.2: Precipitation Gravimetry precipitation 9.2: Precipitation Gravimetry 9.4: Particulate Gravimetry 10.1: Overview of Titrimetry 10.5: Precipitation Titrations precipitation gravimetry 9.1: Overview of Gravimetric Methods 9.2: Precipitation Gravimetry Precipitation Reactions 7.4: Equilibrium Constants for Chemical Reactions precipitation titration 10.5: Precipitation Titrations Precipitation Titrimetry 10.5: Precipitation Titrations precision 4.4: Selecting an Analytical Method 5.2: Characterizing Experimental Errors 9.2: Precipitation Gravimetry 10.2: Acid–Base Titrations 11.3: UV/Vis and IR Spectroscopy 11.4: Atomic Absorption Spectroscopy 11.7: Atomic Emission Spectroscopy 15.2: Verifying the Method 15.3: Validating the Method as a Standard Method 16.4: Evaluating Quality Assurance Data 8 qualitative analysis 2.3: Common Analytical Problems Qualitative Applications 9.2: Precipitation Gravimetry 11.3: UV/Vis and IR Spectroscopy quality assessment 16.1: The Analytical Perspective—Revisited 16.3: Quality Assessment 16.4: Evaluating Quality Assurance Data quality assurance 4.6: Protocols quality assurance program 16.1: The Analytical Perspective—Revisited 16.4: Evaluating Quality Assurance Data quality control 4.6: Protocols 16.1: The Analytical Perspective—Revisited 16.2: Quality Control Quantitative Analysis 2.3: Common Analytical Problems Quantitative Applications 11.7: Atomic Emission Spectroscopy 12.3: Coulometric Methods quantitative estimates 16.4: Evaluating Quality Assurance Data quantitative science 3.1: Measurements in Analytical Chemistry https://chem.libretexts.org/@go/page/211867 quantitative transfer 3.5: Preparing Solutions quartering 8.3: Implementing the Sampling Plan quartz crystal microbalance 9.4: Particulate Gravimetry quench 14.2: Chemical Kinetics S Redox 10.4: Redox Titrations 12.2: Potentiometric Methods Redox Electrodes 12.2: Potentiometric Methods redox indicator 10.4: Redox Titrations Redox titration Redox Titration Curves 10.4: Redox Titrations R 5.8: Using Excel and R to Analyze Data 15.4: Using Excel and R for an Analysis of Variance R for 15.4: Using Excel and R for an Analysis of Variance radiation 11.8: Spectroscopy Based on Scattering radiationless deactivation 11.6: Photoluminescence Spectroscopy radioactive 14.3: Radiochemistry Radioactive Analytes 14.3: Radiochemistry radioactive atoms 14.3: Radiochemistry radioactive particles 14.3: Radiochemistry radioactive tracer 14.3: Radiochemistry radiochemical methods 14.4: Flow Injection Analysis Radiochemistry 14.3: Radiochemistry random error 15.3: Validating the Method as a Standard Method random errors 16.4: Evaluating Quality Assurance Data random sampling 8.2: Designing a Sampling Plan range 5.1: Characterizing Measurements and Results rate 14.2: Chemical Kinetics rate constant 12.3: Coulometric Methods 14.2: Chemical Kinetics rate law 14.2: Chemical Kinetics rate method 14.2: Chemical Kinetics reactant 7.5: Le Châtelier’s Principle reactants 7.5: Le Châtelier’s Principle reaction rate 14.2: Chemical Kinetics reagent blank 15.2: Verifying the Method 16.3: Quality Assessment reagent grade 6.1: Analytical Standards recovery 12.2: Potentiometric Methods sample 5.4: The Distribution of Measurements and Results 13.4: Gas Chromatography 13.7: Electrophoresis Sample Cells 10.4: Redox Titrations R salt bridge 11.3: UV/Vis and IR Spectroscopy Sample Collection 8.3: Implementing the Sampling Plan Redox Titrimetry Sample Distributions 10.4: Redox Titrations 5.4: The Distribution of Measurements and Results reducing agent Sample Introduction 7.4: Equilibrium Constants for Chemical Reactions reduction 11.4: Atomic Absorption Spectroscopy Sample Means 7.4: Equilibrium Constants for Chemical Reactions reference electrode 5.6: Statistical Methods for Normal Distributions sample preparation 12.1: Overview of Electrochemistry Reference Electrodes 12.2: Potentiometric Methods Regression 8.3: Implementing the Sampling Plan Sample Preservation 8.3: Implementing the Sampling Plan Samples 6.6: Using Excel and R for a Regression Analysis Regression Analysis 6.6: Using Excel and R for a Regression Analysis Regression Equation 6.4: Linear Regression and Calibration Curves relative supersaturation 9.2: Precipitation Gravimetry relaxation 11.5: Emission Spectroscopy Repeatability 5.4: The Distribution of Measurements and Results 13.5: High-Performance Liquid Chromatography Sampling 4.5: Developing the Procedure 8.1: The Importance of Sampling 8.2: Designing a Sampling Plan 8.3: Implementing the Sampling Plan Sampling Plan 8.2: Designing a Sampling Plan 8.3: Implementing the Sampling Plan saturated calomel electrode 5.2: Characterizing Experimental Errors Reproducibility 12.2: Potentiometric Methods Scale of Operation 5.2: Characterizing Experimental Errors Residual Current 12.4: Voltammetric Methods resolution 11.1: Overview of Spectroscopy 13.2: General Theory of Column Chromatography 13.3: Optimizing Chromatographic Separations 4.4: Selecting an Analytical Method 11.4: Atomic Absorption Spectroscopy 11.6: Photoluminescence Spectroscopy 11.7: Atomic Emission Spectroscopy scattering 11.8: Spectroscopy Based on Scattering scientific notation 3.1: Measurements in Analytical Chemistry response 15.1: Optimizing the Experimental Procedure scintillation counter 14.3: Radiochemistry response surface 15.1: Optimizing the Experimental Procedure SCOT 13.4: Gas Chromatography retentate 8.6: Classifying Separation Techniques searching algorithm 15.1: Optimizing the Experimental Procedure retention factor 13.2: General Theory of Column Chromatography 13.3: Optimizing Chromatographic Separations retention factors secondary standards 6.1: Analytical Standards Selectivity 13.7: Electrophoresis Retention time 13.2: General Theory of Column Chromatography robust 4.4: Selecting an Analytical Method room temperature 7.4: Equilibrium Constants for Chemical Reactions rugged 4.4: Selecting an Analytical Method ruggedness testing 4.4: Selecting an Analytical Method 10.2: Acid–Base Titrations 13.3: Optimizing Chromatographic Separations 13.5: High-Performance Liquid Chromatography 13.7: Electrophoresis 14.2: Chemical Kinetics selectivity coefficient 4.4: Selecting an Analytical Method 8.4: Separating the Analyte from Interferents selectivity factor 13.2: General Theory of Column Chromatography 15.2: Verifying the Method 8.5: General Theory of Separation Efficiency 9 https://chem.libretexts.org/@go/page/211867 sensitivity 4.4: Selecting an Analytical Method 6.3: Determining the Sensitivity 9.2: Precipitation Gravimetry 10.2: Acid–Base Titrations Separate Mixtures 13.1: Overview of Analytical Separations Separation 8.5: General Theory of Separation Efficiency 8.6: Classifying Separation Techniques 8.8: Separation Versus Preconcentration separation factor 8.5: General Theory of Separation Efficiency Separation Modules 14.4: Flow Injection Analysis SFC 13.6: Other Forms of Liquid Chromatography SHE 12.2: Potentiometric Methods SI units 3.1: Measurements in Analytical Chemistry signal 4.3: Classifying Analytical Techniques 6.2: Calibrating the Signal 10.1: Overview of Titrimetry 11.1: Overview of Spectroscopy 13.5: High-Performance Liquid Chromatography 14.4: Flow Injection Analysis signal averaging 11.3: UV/Vis and IR Spectroscopy signal processor 11.1: Overview of Spectroscopy significance test 5.5: Statistical Analysis of Data Significance Testing 5.5: Statistical Analysis of Data Significance Tests 5.8: Using Excel and R to Analyze Data significant figures 3.1: Measurements in Analytical Chemistry silica 13.5: High-Performance Liquid Chromatography silica particles 13.5: High-Performance Liquid Chromatography silver/silver chloride electrode 12.2: Potentiometric Methods simplex 15.1: Optimizing the Experimental Procedure Simplex Optimization 15.1: Optimizing the Experimental Procedure Single Components 12.4: Voltammetric Methods Single Operator Characteristics 15.2: Verifying the Method singlet excited state 11.6: Photoluminescence Spectroscopy slope 6.4: Linear Regression and Calibration Curves SMDE 12.4: Voltammetric Methods solid 8.3: Implementing the Sampling Plan Solids 8.3: Implementing the Sampling Plan solubility standard deviation about the regression 7.7: Solving Equilibrium Problems 7.10: Using Excel and R to Solve Equilibrium Problems 9.2: Precipitation Gravimetry Standard Error of the Mean solubility product 7.4: Equilibrium Constants for Chemical Reactions solute 13.1: Overview of Analytical Separations solute’s charge 13.7: Electrophoresis 6.4: Linear Regression and Calibration Curves 5.4: The Distribution of Measurements and Results standard hydrogen electrode 12.2: Potentiometric Methods Standard Method 15.1: Optimizing the Experimental Procedure 15.2: Verifying the Method 15.3: Validating the Method as a Standard Method standard operations procedure solute’s radius 16.2: Quality Control 13.7: Electrophoresis standard potential solutions 7.4: Equilibrium Constants for Chemical Reactions 3.5: Preparing Solutions 8.3: Implementing the Sampling Plan SOP Standard Reference Materials 5.2: Characterizing Experimental Errors standard sample 16.2: Quality Control 15.2: Verifying the Method Soxhlet extractor 8.6: Classifying Separation Techniques Specificity 4.4: Selecting an Analytical Method Spectral Interferences 11.7: Atomic Emission Spectroscopy spectral searching 11.3: UV/Vis and IR Spectroscopy spectrofluorimeter standard state 7.2: Thermodynamics and Equilibrium Chemistry standardization 6.3: Determining the Sensitivity Standardizing 10.2: Acid–Base Titrations 10.4: Redox Titrations Standards 12.2: Potentiometric Methods 11.6: Photoluminescence Spectroscopy 13.5: High-Performance Liquid Chromatography Spectrophotometer 11.3: UV/Vis and IR Spectroscopy spectrophotometric titration curve 10.3: Complexation Titrations spectrophotometry 15.1: Optimizing the Experimental Procedure Spectroscopic Detectors 13.5: High-Performance Liquid Chromatography Spectroscopic methods 11.5: Emission Spectroscopy spectroscopy static mercury drop electrode 12.4: Voltammetric Methods stationary phase 13.1: Overview of Analytical Separations 13.6: Other Forms of Liquid Chromatography Stationary Phases 13.1: Overview of Analytical Separations 13.5: High-Performance Liquid Chromatography statistical analysis 5.5: Statistical Analysis of Data statistical control 16.1: The Analytical Perspective—Revisited statistical methods 4.3: Classifying Analytical Techniques 11.1: Overview of Spectroscopy 11.2: Spectroscopy Based on Absorption 11.8: Spectroscopy Based on Scattering 14.4: Flow Injection Analysis spike recovery 16.3: Quality Assessment 16.4: Evaluating Quality Assurance Data splitless injection 5.6: Statistical Methods for Normal Distributions 15.3: Validating the Method as a Standard Method stock solution 3.5: Preparing Solutions stoichiometric 3.3: Stoichiometric Calculations stoichiometric relationship 3.3: Stoichiometric Calculations 13.4: Gas Chromatography SPME 13.4: Gas Chromatography Spreadsheets 3.6: Spreadsheets and Computational Software stacking stoichiometry 4.4: Selecting an Analytical Method 11.3: UV/Vis and IR Spectroscopy stratified sampling 8.2: Designing a Sampling Plan Stray radiation 11.2: Spectroscopy Based on Absorption 13.7: Electrophoresis stripping voltammetry standard 6.5: Blank Corrections 12.2: Potentiometric Methods 15.1: Optimizing the Experimental Procedure Standard Additions 6.3: Determining the Sensitivity 12.2: Potentiometric Methods standard deviation 12.4: Voltammetric Methods strong acid 7.4: Equilibrium Constants for Chemical Reactions 7.8: Buffer Solutions strong acids 10.2: Acid–Base Titrations strong base 5.1: Characterizing Measurements and Results 15.3: Validating the Method as a Standard Method 16.4: Evaluating Quality Assurance Data 10 7.4: Equilibrium Constants for Chemical Reactions 7.8: Buffer Solutions https://chem.libretexts.org/@go/page/211867 strong bases TISAB 10.2: Acid–Base Titrations sublimation 8.6: Classifying Separation Techniques 8.3: Implementing the Sampling Plan 10.1: Overview of Titrimetry 10.4: Redox Titrations 10.5: Precipitation Titrations titrant 10.1: Overview of Titrimetry 10.5: Precipitation Titrations 14.2: Chemical Kinetics supercritical fluid 8.6: Classifying Separation Techniques supercritical fluid chromatography 13.6: Other Forms of Liquid Chromatography Titration 10.2: Acid–Base Titrations titration curve 10.3: Complexation Titrations 10.5: Precipitation Titrations supernatant 9.2: Precipitation Gravimetry surface adsorbates 3.2: Concentration symmetric equivalence point 10.4: Redox Titrations systematic errors 15.3: Validating the Method as a Standard Method 16.4: Evaluating Quality Assurance Data 10.1: Overview of Titrimetry 10.4: Redox Titrations 10.5: Precipitation Titrations titration error 10.5: Precipitation Titrations Titrimetry 4.3: Classifying Analytical Techniques 10.1: Overview of Titrimetry 10.2: Acid–Base Titrations 10.3: Complexation Titrations 10.4: Redox Titrations 10.5: Precipitation Titrations systematic–judgmental sampling tolerance 5.2: Characterizing Experimental Errors target population 8.1: The Importance of Sampling TCD 13.4: Gas Chromatography technique 4.2: Techniques, Methods, Procedures, and Protocols temperature 7.2: Thermodynamics and Equilibrium Chemistry 13.4: Gas Chromatography Temperature Control 13.4: Gas Chromatography Temperature programming 13.4: Gas Chromatography Tempmperature 10.2: Acid–Base Titrations total analysis technique 4.3: Classifying Analytical Techniques total charge 12.3: Coulometric Methods total ionic strength adjustment buffer 12.2: Potentiometric Methods Total Mobility theory 9.2: Precipitation Gravimetry Thermal Conductivity Detector 13.4: Gas Chromatography thermal excitation 11.5: Emission Spectroscopy thermodynamically 7.2: Thermodynamics and Equilibrium Chemistry thermodynamics 13.7: Electrophoresis 9.3: Volatilization Gravimetry thermogravimetry 9.3: Volatilization Gravimetry unpaired data 5.6: Statistical Methods for Normal Distributions unweighted linear regression V validation 4.5: Developing the Procedure 15.3: Validating the Method as a Standard Method van Deemter equation 13.3: Optimizing Chromatographic Separations vanadium 15.1: Optimizing the Experimental Procedure Variance 5.1: Characterizing Measurements and Results 8.2: Designing a Sampling Plan 15.3: Validating the Method as a Standard Method 15.4: Using Excel and R for an Analysis of Variance Variations 13.3: Optimizing Chromatographic Separations vibrational energy level 11.6: Photoluminescence Spectroscopy 11.6: Photoluminescence Spectroscopy Visualizing Data 6.5: Blank Corrections 5.8: Using Excel and R to Analyze Data tracer Vmax 14.3: Radiochemistry 14.2: Chemical Kinetics transducer 11.1: Overview of Spectroscopy transmittance 11.2: Spectroscopy Based on Absorption 11.3: UV/Vis and IR Spectroscopy trip blank 16.3: Quality Assessment triplet excited state 11.6: Photoluminescence Spectroscopy turbidimetry 11.8: Spectroscopy Based on Scattering type 1 error 5.5: Statistical Analysis of Data type 2 error 5.5: Statistical Analysis of Data 7.2: Thermodynamics and Equilibrium Chemistry thermogram 3.2: Concentration units vibrational relaxation total Youden blank theoretical model 15.1: Optimizing the Experimental Procedure 3.2: Concentration unit conversion 6.4: Linear Regression and Calibration Curves titrations 8.2: Designing a Sampling Plan T 14.2: Chemical Kinetics unit 10.1: Overview of Titrimetry Systematic Sampling 8.2: Designing a Sampling Plan Uncompetitive Inhibition 3.2: Concentration Titration Curves 9.2: Precipitation Gravimetry symbolic notation 3.1: Measurements in Analytical Chemistry 5.2: Characterizing Experimental Errors 5.3: Propagation of Uncertainty 6.4: Linear Regression and Calibration Curves 11.3: UV/Vis and IR Spectroscopy 15.1: Optimizing the Experimental Procedure titrand subsamples substrate uncertainty 12.2: Potentiometric Methods void time 13.2: General Theory of Column Chromatography Volatilization 9.3: Volatilization Gravimetry volatilization gravimetric 9.4: Particulate Gravimetry Volatilization Gravimetry 9.1: Overview of Gravimetric Methods 9.3: Volatilization Gravimetry Volhard method 10.5: Precipitation Titrations Voltammetric Measurements 12.4: Voltammetric Methods voltammetric methods 12.4: Voltammetric Methods U Voltammetric Technique ultramicro voltammetry 12.4: Voltammetric Methods 4.4: Selecting an Analytical Method thermometric titration curve 12.4: Voltammetric Methods 13.5: High-Performance Liquid Chromatography voltammogram 10.1: Overview of Titrimetry Time 12.4: Voltammetric Methods 4.4: Selecting an Analytical Method 11 https://chem.libretexts.org/@go/page/211867 Voltammograms 12.4: Voltammetric Methods volume 3.4: Basic Equipment 4.3: Classifying Analytical Techniques volume percent 3.2: Concentration volumetric buret 10.1: Overview of Titrimetry volumetric flask 3.4: Basic Equipment volumetric pipet 3.4: Basic Equipment W Weight percent 3.2: Concentration wavelength 11.1: Overview of Spectroscopy 11.7: Atomic Emission Spectroscopy 11.8: Spectroscopy Based on Scattering wavenumber where 15.1: Optimizing the Experimental Procedure working electrode 12.1: Overview of Electrochemistry 12.3: Coulometric Methods 13.5: High-Performance Liquid Chromatography 11.1: Overview of Spectroscopy weak acid 7.7: Solving Equilibrium Problems 10.3: Complexation Titrations weak acids Z Zeta Potential 7.4: Equilibrium Constants for Chemical Reactions weak base 13.7: Electrophoresis 7.8: Buffer Solutions 12 https://chem.libretexts.org/@go/page/211867 Glossary Sample Word 1 | Sample Definition 1 1 https://chem.libretexts.org/@go/page/279435 Detailed Licensing Overview Title: Analytical Chemistry Webpages: 156 Applicable Restrictions: Noncommercial All licenses found: CC BY-NC-SA 4.0: 86.5% (135 pages) Undeclared: 13.5% (21 pages) By Page Analytical Chemistry - Undeclared 3.7: The Laboratory Notebook - CC BY-NC-SA 4.0 3.8: Basic Tools of Analytical Chemistry (Exercises) - CC BY-NC-SA 4.0 3.9: Basic Tools of Analytical Chemistry (Summary) - CC BY-NC-SA 4.0 Front Matter - Undeclared TitlePage - Undeclared InfoPage - Undeclared Table of Contents - Undeclared Licensing - Undeclared 4: The Vocabulary of Analytical Chemistry - CC BYNC-SA 4.0 2: Analytical Chemistry 2.0 (Harvey) - CC BY-NC-SA 4.0 4.1: Analysis, Determination, and Measurement CC BY-NC-SA 4.0 4.2: 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